It is my experience that the difficulty of a horse to pick up one lead or the other is a symptom of something else, and is not the problem itself. Usually, it is because a horse is very stiff and heavy on one side, and is not supple/comfortable enough to transfer weight to the other side.
Lots of lateral suppling exercizes to get him more balanced on both sides will help. I would work on getting him to flex to both sides, and disengage the hind end and step over.
One of the best things I do with my horse to get him to shift his weight over is doing turns on the haunches (even quarter turns) AWAY from his stiff side, as it forces him to get the weight off that shoulder. I like to do a lot of "squares", where I will walk and halt, and do a quarter turn to get make the turn - so a quarter turn, walk a long side, quarter turn, long side..etc. Once we can do it at a halt, I do it at a walk, and then at a trot. And, I make SURE that the first step from that halt is towards that stiff side.
So, for example, my horse is stiff on his right side (so he would more readily pick up that lead), so if I was tracking right around the square, I want him to take a step to the left, or at least feel him shift his weight to the left, inorder to turn right. I will reverse sides, but I make my horse shift his weight off the stiff side to turn. I will even do a circle, but I am DILIGENT about making sure that when he takes that first step, he does so by shifting his weight to the left side. And, I make sure I keep his right/stiff jaw supple and I constantly communicate with it - much like I would work a rusty hinge. By communication, I mean gentle squeezes (opening and closing my fingers) on the reins. Once they will shift weight to the other side, then it frees up their shoulder TO be about to pick up the other lead. A horse that is well balanced and supple on both sides will generally pick up the correct lead, because it is easier in a particular direction.
Horses that are really stiff on one side often also feel like they are dropping their shoulder and careening around a turn on one leg - because all of their weight is on that shoulder around a turn. You can't fix that problem when you are half-way through with the turn, because all of their weight is already there, but you have to make sure their weight is shifted to the outside before you turn. Same thing with leads... a horse WONT pick up a lead if all of his weight is locked down on one side.
Other good exercizes for getting them to free up their shoulders and become more balanced are correct leg-yeilds (so neither leading in the shoudlers or the haunches) and shoulders-in exercizes. You should be able to use your legs and your seat to get your horse to shift his weight to either leg, or his hind end. Once you can get him to do that, and he is balanced, then the leads are easy.
The other thing I want to add is that if he is consistantly NOT picking up a lead, even on the lunge, regardless of the diameter of the circle, you may want to have his hocks checked out. There are some conditions within the joints in the hocks, like arthritis or spavin, that may make it more uncomfortable for the horse to push more with that leg, and therefore they would be more resistant to picking up that lead.
