My only experience riding a draft was riding a clyde in a western saddle. It was soo much FUN. The lope was like riding a big dog, so much space and time in the air. You can get saddles that fit them but it takes a bit of fitting (ie. Standard quarter horse bars are not going to cut it). I think what people forget (and some will slam me for this but who cares) is that the basics of all riding is the same. The communication and aids all come from the same place. If your horse moves off your leg well and is balanced then really the saddle should be just window dressing.There is no one disciple that is ridden in the hands. I ride western because I find the saddle more comfortable. I have ridden english and sometimes throw the english tack on just for hahas. My standardbreds have no problem going between tack.
I do not show so I can't speak for the reining aspect of western but it might be worth considering. I would not recommend barrels (not because I don't think your horses could do it) but because the mechanics of it are so hard on any horses legs. I would also sort of feel the same way about cutting or bulldogging. I would look into some reining or some of the competitive trail classes they have. I can see that being an area that traditional harness horses would do well at because they have been selected for a years upon years to be well mannered in crowded areas. What I am saying is that I think competitive trial classes would be good for level headed horses. I have not met many (although I have met a few) really hot drafts, most are easy going and take life in stride.
In the end, just because you have trained him for one thing does not mean he can't be trained for another. In my book, the more things he can do the better.
I don't think there is a huge difference in training a horse to go English/dressage and training him Western. At least initially. Both use a snaffle, and both will post the trot and use a light seat until the horse can carry the rider better.
The only real difference is that eventually, you might train for neck reining, and you might sit the trot more, but even that isn't a given.
I think you should do whichever is cheaper, unless you have money to burn.
There was a guy on here who had a Clydey in western tack and the horse looked great. The fellow was like 6' 4' and near 300 lbs, so it made the horse look of a "normal" size. I cant' remember his name.