On a short test ride (15 minutes or so) through city streets, the difference between a hybrid and a mountain bike will be minimal. But as the time increases, you will notice the difference. 3 hours on my hybrid on the streets of Chicago at a decent speed feels like no effort at all. However, 3 hours on my Shogun mountain bike on the streets of Chicago at a decent speed is tiring.
Once winter comes, I'm hoping that my Shogun will earn its keep as a bike that will be useful for riding through snow. If it ends up being a winter that is dry or icy rather than snowy, I'll probably use my hybrid most of the time.