Ask HN: European online payment preferences?

We're implementing online payments for a subscription service used about equally by American and European clients.

We've already decided, for this first iteration, that we'd prefer not to get a merchant account, and that it's acceptable to bill in USD. (I know this isn't an ideal solution for Europeans.)

I would prefer to use a service like Stripe, where we don't have to store credit card data but the payment itself feels 'native' - it seems to take place entirely on our own site.

However, the European developers I work with tell me something like PayPal would be preferable, because the payment forms are not on our site - instead, the user is redirected to a third-party service they're more likely to trust. They tell me that apart from a few large services, this is the way it's done in Europe.

This fascinates me, because in my head, redirecting to a third-party site for payment feels amateurish. But this may just be my preferences as a Canadian who's only worked in the United States, and lacks extensive experience dealing with Europeans.

So, my question, primarily for the Europeans: taking both European attitudes towards security and European attitudes towards aesthetics into account, do you think European small businesses would prefer to pay for a service on that service's website or on the website of a third-party service like PayPal?