I've used both and both are great overall. Even if you are using TensorFlow, I would recommend AWS right now for someone just starting out because the document

I've used both and both are great overall. Even if you are using TensorFlow, I would recommend AWS right now for someone just starting out because the documentation is more currently more thorough, although that will probably change. The CloudML service looks really cool (and I think it's really what everyone will ultimately use), but I hit enough problems/bugs getting my model trained and running that I plan to wait for it to come out of beta before trying again.