The consortium or company running a private blockchain can easily, if desired, change the rules of a blockchain, revert transactions, modify balances, etc. In some cases, eg. national land registries, this functionality is necessary; there is no way a system would be allowed to exist where Dread Pirate Roberts can have legal ownership rights over a plainly visible piece of land, and so an attempt to create a government-uncontrollable land registry would in practice quickly devolve into one that is not recognized by the government itself. Of course, one can argue that one can do this on a public blockchain by giving the government a backdoor key to a contract; the counter-argument to that is that such an approach is essentially a Rube Goldbergian alternative to the more efficient route of having a private blockchain, although there is in turn a partial counter-argument to that that I will describe later.
Always there is a balance in nature, even in blockchains. If you want to have extra features, you need to make a sacrifice from your current features. For example to have high speed and volume; you need to give some from your security & immutability by doing consensus with smaller groups or you need to use different methods in consensus like POS / PBFT. (Proof of Stake / Practical Byzantine Fault Tolerance)
Decentralized web. The sidechain technology holds premises to expand one of the main values of the blockchains – the decentralization of confidence. There is no need for central structure behind the transactions - the holders of cryptocurrencies are free to use their assets the way they want. The sidechains make their deals even more protected and reliable.
Note: Some would argue that such a system cannot be defined as a blockchain. Also, Blockchain is still in it’s early stages. It is unclear how the technology will pan out and will be adopted. Many argue that private or federated Blockchains might suffer the fate of Intranets in the 1990’s, when private companies built their own private LANs or WANs instead of using the public Internet and all the services, but has more or less become obsolete especially with the advent of SAAS in the Web2.
Forbes reports that blockchain and biometric eyeball scanning technologies underpin the systems that support food distribution in the Syrian refugee crisis. While there are many further uses of blockchain, at the core of its business functionality is the creation of transparent, stacking “ledgers” of information. This is where private blockchain can prove extremely useful.
As RSK plans to host all types of clients and smart contracts: financial industry players, educational institutions, large importing companies, government and individuals, which means they are full on attack mode on Ethereum’s business model. There are endless opportunities within a market with unlimited potential and we could now see a first real competitor for Ethereum, that has a big hashrate, secure network, safer environment for developers, much higher throughput and solved scalability issues.
In simple terms, public blockchains can receive and send transactions from anybody in the world. They can also be audited by anybody, and every node has as much transmission power as any other. Before a transaction is considered valid, it must be authorized by each of its constituent nodes via the chain’s consensus process. As long as each node abides by the specific stipulations of the protocol, their transactions can be validated, and thus add to the chain
Third option is to write your own blockchain protocol according to your needs. You will be able to answer all your what if questions if you design it by yourself. Ripple, Hyperledger projects (Fabric, Burrow, Indy), Corda, Multichain and most flexible and popular one Ethereum can be examples of that option. That option is the most costly and risky one. You have to invest a lot, and after you create your blockchain, you have to find people & companies to use it. Also you need to attract community of developers to upgrade, enhance your blockchain for coming requirements in the future. Above blockchains are the ones I remember immediately, also there are others.

Bitcoin se acerca a los 10,000 millones de capitalización, con una infraestructura y usuarios que requieren que todas las ideas e innovación que se desarrolla a su alrededor cumpla con un nivel de seguridad y testeo tan elevados como el propio Bitcoin. Es por esto que, al menos hasta no ser algo totalmente definnido y fiable en la blockchain test de Bitcoin, no se podrá empezar a presionar para una posible implementación en la blockchain live.
Hasta la fecha (Agosto del 2016), las sidechains sobre Bitcoin no son más que algo teórico. Una implementación de este tipo requeriría de un cambio en el código Bitcoin (hay miembros de la comunidad Bitcoin con gran prestigio, como es el caso de Peter Todd, que argumentan que una sidechain, tal y como la describe Blockstream en su paper, no podrían llevarse a la práctica en Bitcoin sin hacer un gran cambio, hard fork, en Bitcoin). En el mismo paper de blockstream se reconoce que una implementación de este tipo, la cual su teoría es simple pero su implementación compleja, se enfrenta a problemas que no está del todo claro que puedan solventarse (y no todos son de tipo técnico).
This type of blockchains can be considered a middle-ground for companies that are interested in the blockchain technology in general but are not comfortable with a level of control offered by public networks. Typically, they seek to incorporate blockchain into their accounting and record-keeping procedures without sacrificing autonomy and running the risk of exposing sensitive data to the public internet.
Unlike the other two-way peg mechanisms discussed in this article, SPV sidechains do not give direct control of real bitcoins on the main chain to a custodian; however, the ability for a majority of miners to produce and build upon fraudulent SPV proofs gives them indirect control over the funds, including the ability to send to themselves. Having said that, there are ways to mitigate this issue.

Public blockchains: a public blockchain is a blockchain that anyone in the world can read, anyone in the world can send transactions to and expect to see them included if they are valid, and anyone in the world can participate in the consensus process - the process for determining what blocks get added to the chain and what the current state is. As a substitute for centralized or quasi-centralized trust, public blockchains are secured by cryptoeconomics - the combination of economic incentives and cryptographic verification using mechanisms such as proof of work or proof of stake, following a general principle that the degree to which someone can have an influence in the consensus process is proportional to the quantity of economic resources that they can bring to bear. These blockchains are generally considered to be "fully decentralized".
Bitcoin’s block interval is ten minutes so it takes about five ten minutes on average for a new transaction to find its way into a block, even if it pays a high fee. This is too slow for some people so they have experimented with alternative cryptocurrencies, based on the Bitcoin code-base, which employ quicker block intervals   [UPDATED 2014-10-27 to correct my embarrassing misunderstanding of mathematics…]
A typical use case for a private blockchain is intra-business: when a company decides to implement blockchain as a business solution, they may opt for a chain to which only company members have access. This is useful if there’s no need for anybody outside of the company to become part of the chain, because private blockchains are more efficient than public and consortium chains. Also, because they are smaller and contained, it is easier for a consensus process or other technical stipulation to be altered on a blockchain. So, for example, if the developers or proprietors want to change the cryptographic method which runs its consensus process, it is much easier to do this on a private blockchain than a public or consortium chain.

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A company called Blockstream has been focusing on these developments and has announced the release of Sidechain Elements, which is an open-sourced framework for sidechain development. It includes a functioning code and a testing environment for working with sidechains with several components: the core network software to build an initial testing sidechain, eight new features not currently supported by bitcoin, a basic wallet and the code for moving coins between blockchains.
The paper outlines some critical developments and associated problems that were both currently trending and forward-thinking at the time, many of them still very much relevant today. At the time, altcoins were quickly gaining prominence and the problems associated with their volatility, security, and lack of interoperability with Bitcoin raised concerns. The paper primarily addressed 6 issues that pegged sidechains aimed to provide a solution:
Function Transactions executed between the locks and unlocks of the main chain tokens don't bloat the main chain. As the technology of a side chain is connected to its main chain, it can be used to build on the developments of the main chain and introduce new features to the market. Child chains serve as the transactional chains of the parent-child architecture, as the parent chain retains minimal features.
Blockchain was invented by Satoshi Nakamoto in 2008 to serve as the public transaction ledger of the cryptocurrency bitcoin.[1] The invention of the blockchain for bitcoin made it the first digital currency to solve the double-spending problem without the need of a trusted authority or central server. The bitcoin design has inspired other applications,[1][3] and blockchains which are readable by the public are widely used by cryptocurrencies. Private blockchains have been proposed for business use. Some marketing of blockchains has been called "snake oil".[9]

The cheapest and most simple option is doing calculations on your local network (off-chain) and integrating with main blockchain by sending the results. It has flaws; you cannot live full advantage of blockchain as we do in bitcoin, because you will still have existing constraints of your current system. Despite all this, it is still a valid option; perhaps you won't need all the features of blockchain technology. Perhaps it is just enough to use blockchain only for your pain points. Factom can be considered under that kind of option. They used bitcoin wisely in their design. They hold the actual mass data in their network and utilize stability of bitcoin in their solution. This project is so successful that at coindesk magazine, it is saying that Factom can be used for the land titles in Honduras.
Since extension blocks can be implemented via soft forks, the features of the extension blocks are essentially opt-in for users. Even in the case of extension blocks with a larger block size limit, users are not forced to upgrade and validate or propagate blocks that are much larger in size. Those who wish to enjoy the level of decentralization offered by 1MB blocks can continue to do so, while those who would like to experiment with much larger block size limits can do so on an opt-in basis.
Blockchain technology can be used to create a permanent, public, transparent ledger system for compiling data on sales, tracking digital use and payments to content creators, such as wireless users [65] or musicians.[66] In 2017, IBM partnered with ASCAP and PRS for Music to adopt blockchain technology in music distribution.[67] Imogen Heap's Mycelia service has also been proposed as blockchain-based alternative "that gives artists more control over how their songs and associated data circulate among fans and other musicians."[68][69] Everledger is one of the inaugural clients of IBM's blockchain-based tracking service.[70]
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^ Jump up to: a b c d e f g h i j k l "Blockchains: The great chain of being sure about things". The Economist. 31 October 2015. Archived from the original on 3 July 2016. Retrieved 18 June 2016. The technology behind bitcoin lets people who do not know or trust each other build a dependable ledger. This has implications far beyond the crypto currency.

“Private blockchains are valuable to solve efficiency, security and fraud problems within traditional financial institutions, but only incrementally. Private blockchains will not revolutionize the financial system. Public blockchains, however, hold the potential to replace most functions of traditional financial institutions with software, fundamentally reshaping the way the financial system works.”