I've made pizzas with fresh mozzarella and with low moisture part skim mozzarella. The common wisdom is the low moisture gives you stretchier, gooier cheese. And also that the fresh can give a soggy crust because of its moisture content.
The way to determine it for myself? Half and half on the same pie. And here it is - a classic Margherita, so there's nothing (much) to distract from the cheese analysis. Note the red spot of sauce at the very bottom. That was my visual marker so I didn't get confused as to which was which.
The results? On the left four slices - low moisture cheese. And on the right four - fresh. The low moisture started bubbling and showing golden oil spots first while cooking in the oven. Eventually the fresh participated as well but as you can see, not as much.
The taste and texture test? Fresh won for both my wife and me. The taste was, well, fresher. The low moisture was notably chewier, dare I say ... more rubbery. Not so with the fresh. A difference that was clear from the start and up until the last bite.
So I think there's no longer any question for me. When I reach for the cheese, it'll be smooth, delicious and fresh. (With exceptions for future experiments and, of course, a judicious use of Danish Fontina!)