I have the new Amazon card reader now. The software seems just like Square, every step of the way. Only difference I noticed is that Square offers receipt options of e-mail or text message, and Amazon only offerers receipt by e-mail (or wireless receipt printer, if you have one).
It deposits the money to your bank account just like Square.
The card reader itself is about twice the length of the Square reader, so cards are MUCH easier to swipe. The Square reader is so short it's easy to rock the card around as you slide the card, triggering a failed swipe.
Bottom line: I like it, and the price is much better!
I've also tried the PayPal system but found their software to be less stable than Square. Amazon's software seems great.