depends with me. When meditating and holding a crystal for extra strength, awareness and focus, I hold it in my left hand and give healing to myself with my right (right-handed here). When giving healing to someone else I do use both hands though (but yes, I use the right a bit more than the left), and there does seem to bit of a difference. Supposedly the left is more Divine feminine energy, and the right more Divine male. As per 'feeling' things during a healing session - my right seems almost more sensitive than my left (but my impression might be warped, as I simply use the right a bit more....)
According to my mother, I was born a lefty but I was made to write with my right hand in school (I don't remember that though). Anyhow, I still write with my right hand but everything else I do as a lefty..with that said...I receive with my left hand, give with my right.