I'm not a medical professional but here are two things I have picked up from reading:
--- Although the exact anatomy of the blood vessels, etc. varies from person to person, it seems that it is easier to do the transplant using the left kidney because the vessels that have to be re-connected tend to be longer (and thus easier to work with) on the left kidney.
--- It appears that the danger of ill effects to the adrenal gland is less if the right kidney is removed.
This being said, the doctors have to look at YOUR anatomy (Ct scan, etc.) to see which might be better in YOUR case. Also if I am not mistaken: when there is a difference in size between your two kidneys they would choose to transplant the smaller kidney and leave you with the larger one.
Hope this helps.
Fr. Pat