I've worked with both Braintree and Stripe, and I'm honestly not sure why people harp on about Stripe so much compared to BT. In my experience, they're both super easy to work with.
Maybe it's a regional thing but I never encountered Stripe in the UK/EU. I don't think people know of it.
Stripe is used by https://pythonanywhere.com I believe they are based in the UK according to their payment statements.
On the other hand of anecdata, I'm in the UK, and plenty of people I know have heard of and use it. It's the developer go-to for most projects I've seen, but BT does appeal with Paypal integration.