Last time I used Stripe it was directly connected to a bank account. They would sit on funds for a couple of days I guess this was to allow the transaction to clear whatever batch cycles happen behind the scenes (debits cards were typically faster than credit charges) but the deposits came directly into the account.
I think it varies by country. Also Stripe isn't available in nearly as many markets as PayPal, two big ones that immediately pop out are Estonia and Hong Kong.
Another thing to bear in mind is lots of people outside the "main Western" countries (for lack of a better term) still don't have credit or debit cards that can be used to pay online. PayPal accepts a lot of local payment methods and even lets you transfer funds from your bank account.
I live in Lithuania (part of the EU since 2004, and Euro since 2015) and only this year have major retailers started to accept cards online. Before that you would receive an invoice and have to make a bank transfer (each bank had their own online payment system merchants could integrate to make it more streamlined) before goods were dispatched. Even now most cards need to be opted in for online payments.
The rest of the world (including a significant portion of EU) still isn't, though. You can sell from basically anywhere with PayPal or FastSpring, not so with Stripe.
That may be true in US and other supported countries but unfortunately here (SE Asia) its not yet available. Stripe needs to support ALL countries to overtake PayPal.
Has that changed?