If the government takes my money, there's process. Not always transparent, but supposedly hewing to some legal process.
If the bank goes under then, in theory, I get back some portion of my deposits thanks to insurance (not always the case, some banks for rich people don't have insurance, but presumably the rich can have people killed or something to make up for it).
But if Paypal takes my money by force or by bankruptcy ... well, so long money. It's just gone and I'm probably not going to see it ever again.
In all cases, I probably signed some sort of contract about the deal. But banks are offering the better contract.
The above is a gross oversimplification, but I don't think its wrong in that. If so, please elucidate.