Do not forget gaited horses are horses, and horses gallop. Gaited horses are just wired a little differently in the brain, plus some to a greater or lesser extent have their conformation tweaked a little also.
It is not often said, but because their hind legs come way up underneath them, many TWHs have a beautiful canter. Well conformed TWHs can gallop, and gallop very fast. Have a look at cowboy versatility events with walkiers on youtube. I would say my TWHs best a most preferred gait is a canter and it is heavenly and very easy even for beginners to ride. She does not like to gallop fast I think because of her shoulder conformation but her half sister who I own adds an extremely atheletic and fast gallop to a beautiful canter.
Some gaited horses are wired very strongly for lateral movement, ie a tendancy to pace. At a canter or gallop their brain will not necessarily keep their legs organised in the steady three or four beat traditional canter and gallop as easily. This is easy to find out on a particular horse. If it has a horrible canter, then it has a horrible canter.
The majority of gaited horses canter and gallop and do so very well but some do not have pleasant or co-ordinated canters. This can also be said of non-gaited breeds.
My experience with Walkers is that they can do just about anything you want, plus a lot you dont, but you just have to ride them right to get all the different alternatives. Unlike non-gaited where you just have the standard walk trot canter, where you just sit there and the horse does it, with walkers you may need to shape the horse to get the gait you want. You may need to actively ride for a gait to get it. You can also get everything else in between.
If you are new to gaited horses go and try out as many as you can of different breeds and within breeds.