Left hand throttles can get you in a lot of trouble quick! I know of one person who died a couple of years back by accidentally grabbing the LHT instead of the brake!!! Last year my dad had the pin out on his LHT after being stuck in some christmas trees after getting unstock he was going down hill and went to reach for the brake and WOT right into a tree and bent his a arm on his 09 XP.
I will agree with a few of the above posts that say they're stronger sidehillers on the weak (left hand side) with/out a left hand throttle. It seems as though you can balance the sled better, where as on the right side with the mountain bar it is kind of a all or nothing type thing.
Bottom Line, it is nice to have a LHT for one thing and that is; A paper weight! No just kidding, hard packed, slow, left handed slopes. Other than that I think that they're worthless!
my .02