Even though I'm right-handed, I always seem to apply my makeup to my left eye much better than my right. My eyeliner is a tad straighter and my eyeshadow perfectly blended on the left eye. And my right eye is somewhat wonky no matter how hard I try.
I use my right hand, and have an easier time applying eye shadow and liner to my left eye, but mascara is easier for me to apply on the right. I think my left eye turns out better most of the time. Great poll!