We went with square a few years ago and couldn't be happier. The base is a little higher, but all cards are the same and still works out well below what normal processing companies charge.
Before changing, I use to love hearing people complain that Amex charges more and won't accept it. In reality, it almost always works out less. You pay the base and transaction fee and that's it. With Visa, you pay the base, transaction fee, plus tier. It's been a few years, but the top tier was almost 14% (never saw one that high, but was always a possibility). As mentioned above, you are paying for the, "miles, cash back, etc.". Add up your visa bill and compare to sales. It typically works out to an average of 6-12%, no matter what they claim. Also, many processors are now charging a fee (mine was $99/year before I switched), to accept debit cards. I do not work for square! We just did a lot of research before we switched.