The anti-Conor idiocy is truly out of control ... Conor is a PROFESSIONAL fighter who has a lifetime of experience getting punched in the face and dealing with it, as well as being a very skilled MMA striker who demolished with his hands plenty of top talented pro opponents and having boxed reasonably ok against arguably the greatest ever around his weight class.
The Paul guy is an "entertainer" who has trained boxing part time for a few years and has just knocked out a completely clueless at fighting athlete from another (non-combat) sport.
Conor would knock him out with ease in the second round (the first he'd feel out the opponent and then showboat a bit).
The ONLY competitive matchups for Paul would be other entertainers/athletes who also train combat sports, or a professional fighter with absolute abysmal striking such as Askren ... and even then he's been hit by far more brutal fighters (Lawler for example) so he would likely be able to take Paul's best shots and strike back eventually.