Ha, reminds me of the movie I just watched... Jet Li's "The One". I'll let you read the description for yourself...
A rogue Multiverse agent goes on a manhunt for versions of himself, getting stronger with each kill. With only one version remaining, he races against the clock to finish him and become "The One."
You'd essentially have an identical twin so god knows if they'd actually be the same as or get along with you. Just depends on how they turn out. They're simply genetically the same, won't change their experiences and circumstances.