That's always the case, between any two parties.
Question is not stability. I guess all good brokers would have a stable platform, minus a few one would have to shed from experience. Question is of suitability. Not everyone offers the same. I trade a bit with Interactive Brokers....ATS is the best in retail BUT for cost, difficult to implement strategies here, I have recently started with Zerodha....ATS via Pi works BUT try a strategy with multiple orders due to scale in, say one add-in order for every point in green and soon Zerodha's low-cost benefit starts looking less attractive.
I imagine similar probs with most brokers. What is needed is an OMS that does no fancy graphics but is a fast & smart routing system, with maybe a screen for semi-automatic, which can be bypassed with due permissions BUT capable of adding data adapters & trader adapters and the problem is solved. One need not shift systems while trading with multiple brokers or while change over from a broker to another.
There are similar other differences between brokers, say of native order types...one may support bracket orders natively or provide a smart large order execution algo, another may not and require you to simulate the order type in your trading script.
Why not quote some numbers here, or in a new thread. Cost of System, Summary of facilities provided, Minimum Trading capital required (with not excessive returns) to afford. Start from a small part time trader to small prop trader, large prop trader etc. Go through normal client, dealer, dealer with ctcl, direct exchange subscriber.
I think it would be useful or at least be educational.