I always just use mirrors, rather than separate algs. I am fairly ambidextrous when it comes to the cube, but only because I forced myself to be so. I've also found that my right hand is better at harder triggers that require a lot of force, and my left hand is better at more delicate finer movements. So for example I can do some triggers consistently faster right handed, like the Z, which for me uses harder trigger moves. But for algs like the T or J perms I can do them consistently faster left handed because they involve finer tuned hand movements. I would do any of these algs either right or left handed during a speedsolve, it's just that one way is consistently faster than the other for me.
I've always thought it was cool. I also cup stack better left handed than right handed.
For the record I am mostly ambidextrous in real life, but I do write with a pencil or pen in my right hand far better than in my left.
Chris