As far as I know Stripe is not a full competitor.
I am end user, and for me paypal usual works fine, and I don't have to worry too much about entering my CC and personal info all over net.
I like the fact, that only Paypal has to know my real name and address, and not every other website I migh want to purchase something from. I don't think there is an option for that with Stripe.
Unless you mean just credit card processing, then sure Stripe can probably do better. But at least for some like me not supporting paypal means site needs to clear higer bar for me to buy something from you.