In-ring- Punk >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Edge.
Mic- Punk >>>>>>>>>>>>>>>>>>> Edge
Face- Punk >>>> Edge
Heel- Punk >>>>> Edge
Character- "Best in the World" > "Rated R Superstar"
Charisma- Punk >>>> Edge
Feuds- Punk/Cena , Punk/Jeff > Edge/Cena , Edge/Taker
Look- Edge > Punk
Before you point and say "LOLZ PUNK MARK" I have to defend myself. Punk is seriously 12x the worker Edge is and I'm pretty sure I don't need to defend myself on that one. In non-gimmick matches Edge sucked balls pretty much 99 percent of the time, and the only OMG CLASSIC non gimmick match that I've ever seen from Edge was with Taker at Mania, and that's not really his doing whatsoever.
On the mic it's Punk by a landslide as well. Punk's pretty much one of the best on the mic EVER IMO , while Edge is just.... EDGE. I liked some of his 2005 and 2006 stuff I guess, but from 2007-2010 and 99-05 he was terrible on the mic. Same old "I AM AWESOME , blah blah blah" Rockstar shit that I never cared for whatsoever. Punk pretty much changed the wrestling landscape with one of his promos. Edge did NOT.
In the face department, it isn't so much that Punk is good as a face that it is Edge being one of the most god-awful faces I have ever seen. His 10-11 face run was fucking TERRIBLE, as well as his earlier run. Just straight up, cookie cutter shit that I didn't care about at all. In 2004 he was booed out of his own hometown for sucking so much as a face, think about that for a second. Punk on the other hand was actually the number 1A face for a year and did pretty damn awesome despite what some may think.
Edge is obviously better as a face than a heel and I loved his early 2006, but Punk easily has him beaten in this department as well. Punk is just a natural asshole who can make you hate him so much, and never needed to use his personal life to garner heat in a situation like Edge needed the whole Lita-Matt affair bullshit. Punk has been the best heel in the world since he turned in 2009, and it hasn't been close whatsoever.
Punk's "best in the world" character is awesome because it can be used in a face/heel/tweener scenario in various ways , either as the cocky motherfucker demanding respect, or the face trying to prove to the world, it works. The "Rated R Superstar" gimmick got REALLY fucking old after 2006, and really peaked on Edge's first title run. Like I mentioned before, it was fucking HORRIBLE from basically 07-11.
Charisma goes to Punk for me. I don't really know how to compare charisma between two as I guess Mic skills would be incorporated into this as well as other factors, I always felt Edge extremely overrated charisma during his career also.
When it comes to feuds, it isn't close whatsoever. Edge's feud with Cena sucked balls and even when I was heavy into the TV product I didn't care for it whatsoever and felt like it was so overdone over the years and so counterproductive. They tried to make Edge/Cena the new Austin/Rock it seemed like and it failed miserably. Punk/Hardy was extremely compelling stuff that actually made JEFF HARDY interesting to me, and Punk/Cena is one of the greatest feuds of all time (The Rock/Austin of this generation, except better matches
Sure, Edge has a better look than Punk, but don't take this and say I'm just a blind Punk mark. It's less of me being a Punk mark and more of me believing that Edge is the most overrated wrestler of all time, trust me. The guy was good for me during like a three month period in his career, the rest of the time I just wanted him off my TV screen.