Considering the fact that you are in fact right handed it seems likely that your more neurally efficient at recruiting your right glute as opposed to your left in preformance of a particular lift whether unilateral or bilateral.
The trauma in the muscle caused by a training stimulus may not be equal even if the same number of repetitions are preformed in a unilateral lift. This is because in your case it seems likely your muscle recruitment pattern from left to right differs. That is, while on one side you may be able to activate your glute to a large extent to complete a lift on the left it may be less active and thus less muscle damage is caused to it.
Many other factors might be involved including tempo and speed differences from side to side. Recall a faster lift recruits more high threshold motor units.
Also, it is possible to produce more force then is strictly required to complete a lift on one side as oppossed to the other. For instance, my left may be capable of producing 110 lbs of force to complete a 100 lbs lift, but my right is capable of producing 120 lbs of force to complete the same lift. Obviously my right is preforming more work even during the course of the same number of repetitions in a unilateral excercise. Of course this in itself will affect the speed of the lift and that might be a good indicator for you to keep track of.
Finally, for a recomendation. I advise you to make single limb work a more substantial part of your workouts especially for a while to help you address any imbalances. Single limb excercise that emphasize the glute are even better as this will assure that your left glute isn't slouching. In fact, I would eliminate any and all bilateral leg work for perhaps the next 8-12 weeks. If you want to throw in an occassional set of deep squats or something of that kind that's fine, but idea is to signficantly restrict this type of work.
In preformance of your single limb work be sure to lift on each side with the same tempo and speed. Also, try to notice any difference you feel in lifting technique from side to side and try to even out any disimilarities. Focus on that left side.
For some ideas on single limb excercises consult the following (I just did a brief search of the T-Nation site and I am sure there are other resources available as well):
I hope this helps.