Nothing will rat a horse out about his level of training better than loping. Most horses will walk and trot reasonably well, without putting up much of a fuss, but when you ask them to step up to the lope, their true colors come out. If the horse is disrespectful and lazy, he’ll ignore your cues. If he’s bad-minded, he’ll kick out and pin his ears when you put your leg on him. If he’s hot and reactive, he’ll take off as soon as you cue him into the lope. And if he has bad brakes, he won’t stop.
To me, there’s no better way of seeing how well a horse is trained than seeing what he does at the lope. It’s a dead giveaway about his attitude and his willingness and how much training he has had.