In high school I worked for a family friend who raised mules with her husband. They bred saddle mules for elk hunting outfits out west, and they were spectacular animals.
The thing about mules isn't that they're stubborn, it's that they're smart. Horses are usually too dumb to realize that what you're asking them to do is something they don't want to do, and if you do something to tick off a horse they usually forget. Mules know what's going on, and they remember. If you have the patience and understanding to work with them that can be a good thing, but it's challenging for sure and can sure be frustrating if you come to an impasse and communication shuts down.
Even at their worst, though, I'll take a mule over a donkey any day. Their breeding jack was a real piece of work. I used to have to mow down his paddock with a weed eater, and they told me that if he ever got out of his stall while I was in there to drop the weed eater and jump the fence. They had to get the fencer turned back on in a hurry because if he got loose he'd kill every male animal they had.