I've used all three: grated, sliced and cubed. I prefer the grated.
When I first started I used sliced. I felt that was the most authentic and traditional way of doing it, i.e. Pepe's. Over time I adjusted my slicer to what I considered to be the best thickness. The cheese (local--Calabro) browned very nicely, had excellent taste and was "super stretchy," a characteristic that all of my family (and other tasters) enjoyed. I always felt that slicing breaks the smallest amount of protein chains and in a sense makes the cheese stretch further before breaking. Shredded's chain are exactly that, shredded. Biggest problem was getting a semi-even 50/50 part skim/whole mix. I'd get a blob of oily, buttery cheese and a blob of firm, mild flavored cheese.
I've used diced a couple times. Melting and browning was good but as others have stated, toppings and cubed really don't mix. I had trouble controlling the burning of my sliced meats (pepperoni, prosciutto) and opted to switch to grated next.
Grated seems to be the best overall. I can control the thickness of cheese more uniformly than with the sliced or cubed. Toppings, melting times and browning are no problem. The only hassle is the amount of time and work it takes to grate a couple of pounds of mozzarella. Usually I can pawn it off on someone else with a "well if you don't help me grate it I can't make pizza!" line. Biggest problem with the grated is that once the cheese is grated, it needs to be used quickly (within a couple days), especially the whole milk. It ends up as a big soft glob otherwise.