My horses are crosses, not pure draft, but they are night and day difference to ride between the two of them, so I thought worth the mention.
My gelding, Claymore (part Clyde, the one in my avatar) had a real jackhammer trot when I got him. He was green when he came to me and had not been taught to collect or move properly, and with some training he has learned to be much lighter on his feet, so it's decent now. Not great, but certainly tolerable. His canter is still a work in progress, some days it's perfect, smooth and collected as can be, other days it's just "hang on and hope there isn't a fence nearby" because he pounds the ground for all he's worth. Like I said, still a work in progress. He's very eager to go-go-go! A single kiss is all it takes to transition from walk to trot and trot to canter.
My mare is a different story. She's half Shire, and while we have had off and on soundness issues with her last year, I'm crossing every finger and toe to hope she is past all that now - because she is a great ride. Her trot is like gliding, I actually had to have someone watch me riding to make sure she wasn't somehow gaited, it is THAT incredibly silky smooth. Her canter, if possible, is even more delightful, easy, rocking horse style that feels like floating. When I got her, she had just been a broodmare all her life, never been broke to ride, but I had her riding easily with only about 3 hours on her back, and took her off the property for an extended trail ride after only about 10 hours on her back. Moving in a balanced, collected way seems to be just innate with her. She'll never, ever win any speed competitions, but she's dreamy to ride. She's super willing to do anything you ask, but she's much more laid back of a personality than Claymore is.