I don't think you can generalize on these matters.
You didn't indicate at which stage the dough is allowed to rise, for example, right after it is made or just before shaping into a round after a reasonable period of fermentation, but all else being equal, and assuming that the dough is not on the verge of overfermenting, I would say that the dough with the longer rise will be better in just about all respects (handling, fermentation, etc.) than one with a lesser rise. But it is quite possible, and perhaps likely, that you won't be able to tell the difference. You should be able to tell the difference between a dough that is given, say, one hour of room temperature fermentation and one that has had several hours of room temperature fermentation and, similarly, one that has had a few days of cold fermentation, but one hour differences may not be detected.
If you are talking about punching the dough down just before using, and that you are not re-kneading the dough, then so long as you are fairly gentle in punching down the dough, you perhaps will be OK. Re-kneading the dough is generally a bad idea because it rearranges the gluten structure and causes the dough to become very elastic and hard to shape. I prefer not to pound the dough in shaping it because I want to keep the gasses in the dough intact so that I get a decent oven spring when it hits the oven. I have seen professionals handle their doughs fairly roughly without noticeable harm but I suspect their doughs are of better quality than mine and can take the rougher handling. Also, their ovens are better.
I also don't think you can generalize across different styles. For example, a standard dough can perform differently than a deep-dish dough or a cracker-crust dough. Some principles are shared in common but there are also differences.