They were one of the first to allow accepting of credit card without leaving the site or requiring heavy PCI compliance work. They did it using client-side toke

They were one of the first to allow accepting of credit card without leaving the site or requiring heavy PCI compliance work. They did it using client-side tokenization so the server never needed to see the credit card data. Paypal either required you to leave the site or put you in territory where you need to meet fairly expensive PCI compliance rules. So the UX was simply better for the buyer. And the API is drop-dead simple to implement. Now a days PCI caught up and requires some compliance for users of Stripe like platforms but still nowhere near as much as the ones who see the card. Also, being able to be up and accepting payments in less than 15 minutes is pretty great. And as other's pointed out, Paypal has (had?) a nasty habit of taking people's money. To be fair I know some stripe merchants where Stripe held back payments as protection against chargebacks. But that is just a delay, not flat out taking the money like Paypal used to do.