In my experience, the gait smoothness of a draft horse depends greatly on their conformation and ranges widely throughout a singular breed, just like any standard sized horse. Some are smooth and some are...not.
The gaits do tend to be a bit bigger and longer. For example, when I was riding my perch gelding, we could be loping across a pasture in a gait that was pretty darn slow for him, but the quarter horse my Dad was riding was galloping pretty fast just to keep up with us just because John's stride was so much bigger and covered more country.
Other than that, the biggest difference between them and a regular sized horse just has more to do with how big they feel between your legs and how high off the ground you are.
The very first time I rode my 18 hand Perch, I had flashbacks to being a very small girl (about 5 years old) and riding on my old stout roping horse. John made me feel like a little tiny thing sitting up there on him.