The answer depends to a large extent on what you want to do, including the type of pizza you want to make. In my opinion, a food processor does best for a small amount of dough, that is, an amount of dough that is too little to make in a stand mixer. It is less effective for large batches of dough, even for a 14-cup food processor. For a normal dough, I also think that a food processor works best at a dough hydration value of about 59-63%. Below that, the food processor may have a hard time kneading the dough, especially if the amount of dough is fairly substantial, and above that, the dough may be too wet and you may end up with the blade spinning but not doing a good job kneading the dough.
From a style standpoint, I think a food processor is a good choice for, say, a NY style dough. In that context, and for a few operational tips, see the thread at http://www.pizzamaking.com/forum/index.php/topic,2189.msg19289.html#msg19289
A food processor is also very good for low hydration doughs where the hydration might be as low as 35%, and where you are trying to achieve a cornmeal effect with the dough. An example of such use, for a cracker-style dough, see Reply 8 at http://www.pizzamaking.com/forum/index.php/topic,5762.msg49042.html#msg49042
I have also been known to use both a food processor and a stand mixer to make a dough. An example of this combination is discussed at Reply 204 at http://www.pizzamaking.com/forum/index.php/topic,9068.msg97757.html#msg97757
Subject to the inherent limitations of a food processor mentioned in the above posts, there is very little that can't be done to make pizza dough in a home setting.