Fully agreed. I just implemented Stripe to take payments for my consulting business online, and it's really nice. My only complaint is that Stripe takes a week to initiate a bank transfer, rather than Square's one business day.

I think right now there's a large difference in culture. Square is really hip and tries to avoid exposing 'nerd stuff' to their users, whereas Stripe focuses heavily on API examples etc. Seeing them combine but stay two different 'personas' could be beneficial for both.