A stock split is merely psychological, a blockchain split is not. Marketing is mostly psychological and having two versions of Bitcoin hinders mainstream adoption of Bitcoin. After a stock split you do not have two versions of the share certificates in circulation. That said, everyone can agree there is a scaling problem and but no one can agree on the solution.
Here is another view on the Bitcoin Unlimited (BU) forking by Vinny Lingham which he points out will further increase the concentration of consensuses power/control to the miners: https://vinnylingham.com/the-power-of-the-invisible-hand-56efaedfb544#.s0eegwyyy
This article is very good at explaining the BU vs. SegWit (Segregated Witness) in simple terms.
A very recent (in the last 2 weeks) new 3rd solution: This 3rd solution is being labelled/called “Super UASF” (User Activated Soft Fork). Super UASF is interesting in that it does not require a hard fork and the majority consensus is captured and decided by the Bitcoin Exchanges and not by the Bitcoin miners! Miners would have no choice but to support the chain that the economic majority wants, at least if they want to be able to continue to sell the bitcoins that they win from mining. Search for: “Bitcoin Super UASF”.
Currently, the “fork” debate has 3 solutions from 3 Bitcoin groups:
The “Core” developers (SegWit), the miners (BU) and the Bitcoin economy/users (Super UASF). Ideally consensus would come from the later, the Super UASF solution.
Personally, I was all for BU, but now that I have learned how it further concentrates the consensus power/control to the miners, I am not for it at all. It removes the 1MB block problem by creating another problem. I don’t like how the “Core” developers seem to control Bitcoin’s future and their SegWit solution needs 95% of the mining hash power to make this consensus decision possible (which is why it hasn’t and probably never will happen). I like this new 3rd solution “Super UASF” that has recently been born, research that solution!