Stripe has been developed for web users not by banks just moving bank apps to web. Their APIs are easy to use and understandable and they have support for lots of languages.

They are also incredibly flexible and it's possible to do things with Stripe that other providers don't allow (for example implementing annual billing it's difficult to get authorisation as a start-up - even if it's only $20 a month, that's $240 annually which means there's a year to charge-back - so implement it as a one off payment, which does mean doing annual billing yourself, but there's a year to get it right).

They also have fantastic start-up deals (if you know the right accelerator or other provider) easy to get transaction fees waived.

They also have engineers at hand to help you with any issues, who actually know the product.