Answer: If you're trying to compare credit card rates by brand--MasterCard, Visa, Discover or even American Express--you are going about it the wrong way. The difference in rates is not in the credit card brand: the difference has to do with your credit rating, what you will be using the card for and which financial institution is offering the card.
For example, qualifying for a card with bad credit is nearly the same regardless of whether it is Visa, MasterCard or Discover. Similarly, if you have excellent credit, the same applies. The next variation in credit rates is whether there are rewards of any type for cash back, frequent flyer or anything else. Any card with any type of reward program will have a higher interest rate simply because a card issuer is not going to give away rewards without gaining something back.
The final basis of comparison is not the brand of card but the card issuer. For example, generally you will find a credit card issued by a credit union will usually have a purchase APR lower than that of a major bank. Be aware, too, that when comparing purchase APRs, you shouldn't be swayed by a promotional APR. These are designed to lure you into getting the card, but after the promotion period ends, you'll be paying a significantly higher APR for as long as you have the card.
My recommendation is to go to CardRatings.com and look for a card that fits your specific needs. Determine if you want cash back or any other reward, what your credit situation is (such as a student or business person) and only then compare offers (but not promotions). You might also keep your eye out for what type card is accepted at most of the places you frequent. That would be about the only reason to choose one brand, such as Visa, MasterCard, or Discover, over another.