This is not uncommon. I have heard of several stories of the children "arguing" over who gets to be the one.
I am assuming you have done the blood tests only and on an HLA scale you are both about equal. In that case, you may want to list the other criteria that come into play when becoming a donor. You can take into account family stability, insurance,time off from work, finances, spouses (is there a spouse who is more uncomfortable with the decision), dependents who rely on you. You can also think about health issues, has anyone already had surgery, any history of illnesses etc. You can also ask to meet with the social worker and maybe after speaking with you they can shed some light on this decision.
While the donor may get the accolades it takes more than a kidney to help a patient with renal failure. The other sibling who does not donate can certainly be available to help care for the sibling who does donate. They will need help after the surgery with household chores, shopping, meals, child care if necessary etc.
If not a good old drawing straws is a plan. But make sure you know if the short straw "wins" or "loses".
Sherri