It's not like you're storing card data because you're using Stripe. Stripe also allows 3D Secure to be used, so Stripe is clearly the more secure option compared to PayPal.
(I've heard that Stripe can do checkouts on it's own domain, but I haven't seen it on a real website)
And as for 3D Secure -- it has no benefit for customer, just an extra password to remember. I am not sure why banks waste time implemeting it, when other systems (like real-time notification of charges on my cell phone) would be significantly more useful.