I was told the battery in the moto x is different between carriers . Is this true
I am not sure who told you that, but that does not sound right. The only thing that changes by carrier (for the Moto X) is the cellular radio in the phone. Everything else (as far as hardware goes) should be the same. So the answer is “no,” that is not true. Hope that helps!
You may want to review Moto X Battery Replacement - SUCCESS! … (note: the replacement of Moto batteries is no small task), but others have been successful and this user shares his success with the rest of us …discussion also includes links to batterys