The drivers
Stock split: The basic motivation behind most stock splits is to lower the price of individual shares of a stock to bring it within the financial reach of retail investors.
One of the best-known examples of a stock split in recent years is the 7-for-1 split of Apple shares in 2014. Prior to the split, when Apple was trading around $700, it was often debated whether the individual stock price was too high. A steep rise in share price in the months that followed seems to have settled the debate. (At least in the case of Apple.)
Bitcoin: The reasons for the split into two cryptocurrencies are complex, but they have nothing to do with ease-of-access for retail investors.
The crux is this: A long-standing debate has divided the bitcoin community on its technical roadmap – specifically, about finding the best way to cope with a growing user base and rising transaction volume.
After the bitcoin fork, bitcoin is still trading at over $2,700, roughly the same price as before. The price of the new asset, Bitcoin Cash, is around $200 to $450 depending on the liquidity of the exchange it's being traded on. In short, the two assets now have two separate values, each derived from their technical roadmap and supporting communities.
Both could end up expensive for investors, but to the extent that one may end up affordable, it may not make it valuable.
Governance
Stock split: In the broadest sense, stock splits and blockchain splits share one thing in common: they must be approved by someone. So who approves them?
Publicly traded companies are owned by their shareholders. Those shareholders then elect a board of directors to act as their proxies in corporate governance issues. The board of directors hires managers to run the company. The board of directors and management, which often overlap, make decisions about matters that are crucial to the functioning of the company. (In theory, this permits companies to behave as rational actors; in practice, less so.)
One of the most important decisions that management and boards of directors make about the public companies they run concerns the makeup of the capital structure, which is the category into which share structure falls.
Bitcoin: Bitcoin is a shared account of value without centralized authority or control. There is no single third party that verifies the accuracy of the value accounted for in the ledger. There is no central governing authority; instead, decisions are made by consensus based on miners (or nodes) signaling their approval for proposals, based on predetermined thresholds for passage that are embedded in the code.
In the event of a split, every actor gets to make decisions in their best interest.
Right now, some exchanges aren't listing Bitcoin Cash, some are. Some miners aren't mining the new blockchain, some are. And some users are trading both, in that both are now digital assets that can be sent seamlessly around the world. Where they go from there will take coordination, but for now, decision-making is isolated and dedicated by self-interest.
Final takeaway
Stock split: A stock split is a corporate action that divides existing shares into more shares without changing the underlying claims on assets that those shares represent. If you double the amount of something, but cut its value in half, you haven't effectively changed the underlying economics at all. (Which is worth more to you: a $20 bill or two $10 bills?)
But here's what really matters about a stock split: no new entity of any kind is created. The same corporate entity that existed before the split still exists afterward.
From an operational standpoint, nothing has been added and nothing has been taken away.
Bitcoin: When Bitcoin Cash split off from the bitcoin blockchain it created an entirely new blockchain unique to Bitcoin Cash. From this point forward, the two currencies will trade under separate symbols. And they will each have their own transaction history after the time of the split, and develop unique values.
Both may fail, both may thrive. That's up to individual actors in the marketplace.
And the ongoing popularity of ethereum and ethereum classic shows just how long it can take for the market to decide – if it will pick one winner at all.
