I joined a startup for stability once. It was way more stable than the megacorp I left.
Megacorp: The company won't disappear overnight, but you might get tossed around different positions and have projects you've spent a year on shut down out of nowhere.
Startup: The company itself may shut down, but in the meantime everything is more focused and transparent.
The worst thing that most big companies do is continue to employ good people on long death marches.
Easy to end up on a soul-destroying maintenance project that you can't leave because it's business-critical and nobody else wants to do it.