All things being equal medically, if a person is going to donate a kidney is there halachic or hashkafic reason to presume donating one kidney would be better than the other?
Someone once asked the Baba Sali which of his kidneys he should donate to a Jew in need of a transplant. After all, Chazal teach that one kidney provides good advice, while the other is somewhat of a yetzer ha-ra. Presumably, the right kidney is the yetzer ha-tov; should he keep that kidney for himself or give it to his fellow Jew? Perhaps it would be wrong to give his left kidney, his yetzer ha-ra, to someone else! The Baba Sali said that he should, in fact, give his left kidney. The very fact that he chose to be moser nefesh for someone else would change his yetzer ha-ra into something good!
(I assume in the ma'aseh that all things were equal medically).
Thanks for the above comments on medical preference. Just to extend that a bit -- even if there was zero medical preference on the kidney's utility for the recipient (which is likely incredibly rare), my next thought would be about the long-term health of the donor -- is s/he will only have one kidney, an injury to it would be life-threatening. Thus, on which side is a kidney likely to be better-protected from damage? (Probably ask a trauma surgeon what they see most often.)