If a world does orbit in the Alpha Centauri system, it will most likely be a super earth with gravity times our own. Here's my reasoning, the interstellar accretion disk that obited Alpha Centauri A was massive, so massive it produced two additional stars!!! So, the system was probably full of super Jupiters that have since been ejected. Any thing that survived, especially if one of those super Jupiters didn't spin inward, would be worlds with great metalicity and mass!!!
My guess that any earth-like world there will be massive and more Venus like than Earth like.
Alpha Centauri B, on the other hand, if it evolved like our jovian worlds, but was simply more massive, would have a stable planetary system with terrestrial worlds probably similar to our's.
Or, I'm totally wrong and Alpha Centuari B was captured and Promixa Centauri is just a coincidence that it appears to have proper motion of the Centauri system.