Most of Paypal's competitors weren't wiped out by Paypal being good, they were wiped out because they weren't as good as handling risk and fraud as Paypal. They got wiped out by criminals.
Paypal is risk averse, which means you shouldn't use them for cases where you're taking a large amount of money up front and not delivering in the near future (i.e events, crowd-funding), or alternatively get pre-approval from Paypal.
I've no idea what the current fraud level against Stripe is, but as they become more mainstream they're going to need to employ more anti-fraud and anti-risk measures as their exposure increases.