I've been making the same recipe for Chicago thin crust for almost 11 years now, and I can say without a doubt that a longer, cold fermentation ("slow rise") is much better. For one thing, a fast rise (same day ferment, a few hrs or so) has many "off" flavors of yeast fermentation, IMO. Moreover, it is a LOT less digestible for me. I feel bloated after eating fast rise crust. Fast rise crusts were more unpredictable in baking, too. I tended to have to stay on top of bubble popping, etc.
Slow rise, however, takes care of these problems. Almost never bubbles, much easier to digest, better flavor. Ideally, I like to make my thin crust 72 hrs before baking. It's stored in the fridge and punched down a couple times the first 12 hrs (and maybe sometimes a third time). I've had great success and pretty consistent results with anything from 48-96 hrs. At 120 hrs, it got crackery (in a good way), and 144 hrs was like a tortilla. Didn't even want to brown at that point. Of course, local conditions vary. I like 72 hrs best, overall, given my recipe. YMMV. But I won't make dough in the morning and then bake it that night. It's just an unpleasant waste of my time and resources at that point.