You handle it simply.

Tell them both that you'll be making decisions on the character, and that your word is law. 

If the first one leaves, after you accept the 'similar-but-not-quite', that's probably someone you don't want anyway, as they could easily turn into the type of player that threatens to leave any time they don't get their way.

If you think the second one is too similar, request the changes to make them different and see where it goes. 

Essentially, you're the GM, your word is law and they have to respect that. Just stand up to them, as otherwise, they'll run all over you... repeatedly.