Honestly, the only problem I ran into with Stripe ever was administrating subscriptions. IIRC even via the API there were a lot of limitations with what state you could put a subscription in, limiting our ability to seamlessly transition from Recurly to Stripe; we ended up duplicating a lot of the subscription logic in the end.
I know subscriptions have been significantly rehauled since then, but this was my only gripe. Stripe was absolutely excellent back when I used it.
