Which do you prefer? Emme or Emi. Both pronounced like Emmy. This would be the nickname for our daughter Emily?

We don't like Emmy because it's the same spelling as the award. We want to give her a name that she can use when she's older like Emily but will be calling her by a nickname as a baby. We were just wondering what most people thought about Emme or Emi if they're going to be pronounced the same.