No one wants to be compared to someone else—especially if the comparison is made between you and your closest friend. It's even more upsetting when the "constructive" criticism is coming from your girlfriend.
If she starts making comments about how you should look or act more like him, it's likely she has a thing for him, and she's dropping not so subtle hints about her intentions. Have an honest conversation about your doubts and fears, and her feelings.
Regardless of what the outcome, you're the one who'll come out winning. If you leave, you're taking your best friend with you.