Well, first off (and this is definitely my own personal prejudice, not gospel), I'd say any cheese made by Kraft is generally going to be inferior. That said...
The mozzarella used by pizzerias is typically of the whole-milk variety; whereas most supermarkets, especially if you're not in a large metro area, usually only stock the part-skim variety. This is stringier, chewier, drier, etc. Also, depending on what kind of pizza you're trying to replicate, many, many pizzerias use a cheese blend, not just mozzarella. For instance, fontina and provolone melt differently than mozzarella. If you can't get whole-milk mozz, you might try blending in some fontina, provolone, or other Italian "melting" cheeses, assuming you can get those.
If you're trying to duplicate a certain type of coal-oven or wood-fired NYC pizza (e.g., Grimaldi's, etc.), you'll need to use fresh buffalo mozz.
If you're trying to replicate a Chicago-style deep dish pizza, you'll need feedback from somebody else, as this is not really pizza in my book!