I think you're asking a very tough question - hence the lack of answers
What are the limitations?
Just because a Thoroughbred is bred to race, doesn't mean each and every one of them will make a great race horse.
Just because Warmbloods are bred to jump and do dressage, doesn't mean they are all good at it.
I know of a very cowy Standardbred... even though he was bred to just race, doesn't mean that this is his only talent.
Canadian horses are known for their sturdy build, strong legs and feet, good bone, they are sociable, intelligent, sensible, trainable, and calm.
Canadians are mostly used for driving but are very versatile and also used for under saddle work: dressage, jumping, eventing, endurance, trail, ranch work or just being the family or kid's horse.
... and each and every one of them may have a talent in one or more of those diciplines.
Limitations? I dare to say that you will never see a Canadian horse race against Thoroughbreds or jump at an international Show Jumping event... but with the right training, they can sure compete in local shows at any dicipline - just like ANY other horse breed too!
You have probably read all the info on Wikipedia already, but here's the link, just in case: Canadian Horse - Wikipedia, the free encyclopedia