If your horse cross canters under saddle and you are going around a corner you can feel the imbalance. If the horse is on the correct lead in front and the outside lead in back, they can't get that inside hind under them for that nicely balanced bend. In the opposite, with the front lead wrong and the hind correct, the horse is going to pop the shoulder to the outside which is also going to cause an imbalance in the turn.
Now, my horse, on the lunge at least, if he gets a burr in his tail about something and decides he wants to try and yank me off my feet, he will swap in front and then pull to the outside. He has a lot more leverage being on that outside lead in front at that point :) and he is really good at doing it with no forewarning. He'll be cantering nicely and then just swaps and goes sideways.
I also notice that if my horse cross canters he tends to kick himself in the leg. This probably happens due to the stride in the canter and the cross action.