Updated list:
Avenger wins:
Beast, Black Panther, Captain America, Daredevil, Dr.Strange, Falcon, Quicksilver, Rulk, Scarlet Witch, Thing, Thor, Valkeyrie, & Vision beats Namor (Pheonix powered [P5]) (AvX #8)
Black Panther beats Storm (Uncanny X-Men #13)
Black Widow beats Dr.Nemesis (Uncanny X-Men #13) *Happened off-panel
Captain America beats Cyclops (AvX #2)
Captain America beats Gambit (AvX Versus #2/AvX #4/Wolverine & the X-Men #11)
Captain America beats Warpath (AvX #4)
Iron Man beats Magneto (AvX Versus #1)
Iron Man droid beats Cannonball (X-Men Legacy #267)
Iron Man droid beats Frenzy (X-Men Legacy #267)
Iron Man droid beats Gambit (X-Men Legacy #267)
Iron Man droid beats Mimic (X-Men Legacy #267)
Iron Man droid beats Shadowcat (X-Men Legacy #267)
Rulk beats Colossnaut (Uncanny X-Men #11 & AvX #2) *Colossnaut lost intentionally
Rulk beats Psylocke (Uncanny X-Men #13)
Scarlet Witch beats Magik (Phoenix powered [P5]) (AvX #7)
Scarlet Witch beats Namor (Phoenix powered [P5) (AvX #7)
She Hulk beats Hepzibah (Uncanny X-Men #12)
Thing beats Namor (AvX Versus #1)
Thing beats Sunspot (Uncanny X-Men #12)
Wolverine beats Kid Gladiator (Wolverine and the X-Men #12)
X-Men Wins:
Angel beats Warmachine (Wolverine and the X-Men #12)
Colossnaut beats Spider-Man (AvX Versus #2) *Spider-Man just left
Colossnaut beats Thing (AvX Versus#3)
Cyclops (Pheonix powered [P2]) beats Hawkeye & Thing (AvX #10) (Oh and rocks Thor at the same time 😉)
Cyclops (Pheonix powered [P2]) beats Iron Fist (AvX #10)
Cyclops (Pheonix powered [P2]) beats Iron Man (AvX #10)
Cyclops (Pheonix powered [P2]) beats Iron Man (AvX #10) *Alternate probability
Cyclops (Pheonix powered [P2]) beats Scarlet Witch (AvX #10)
Cyclops (Pheonix powered [P2]) beats Shao Lao (Infant) (AvX #10)
Cyclops (Pheonix powered [P5]) beats Thor (AvX #3)
Cyclops (Pheonix powered [P2]) beats Thor (AvX #10) *Alternate probability
Cyclops (Pheonix powered [P2]) beats Wolverine (AvX #10) *Alternate probability
Dr.Nemesis beats Quicksilver (AvX #2)
Havok & Polaris beats Vision (AvX #7)
Hope beats Wolverine (AvX #2)
Kid Gladiator beats Giant-Man (Wolverine and the X-Men #12)
Kid Gladiator beats Quicksilver (Wolverine and the X-Men #12)
Magik beats Black Widow (AvX Versus #3)
Magik beats Dr.Strange (AvX #2-3)
Magik (Pheonix powered [P4]) & Colossus (Pheonix powered [P4]) beats Spider-Man (AvX #9)
Magik (Pheonix powered [P4]) & Colossus (Pheonix powered [P4]) beats Thor (AvX #9)
Namor beats Cage (Uncanny X-Men #12)
Namor (Pheonix powered [P5]) beats Thor (Wolverine and the X-Men #12)
Namor (Pheonix powered [P5]) beats Thor (AvX #8)
Namor (Pheonix powered [P5]) & Colossus (Pheonix powered [P5]) beats Gladiator (Wolverine and the X-Men #13)
Rachel Summers beats Black Widow (Wolverine and the X-Men #12, Avengers #29)
Rogue beats Falcon (X-Men Legacy #267)
Rogue beats Iron Man droid (X-Men Legacy #267)
Rogue beats Moon Knight (X-Men Legacy #267) *MK lost intentionally
Rogue beats Ms.Marvel (X-Men Legacy #269)
Rogue beats She Hulk (X-Men Legacy #267)
White Queen (Pheonix powered) beats Hawkeye (AvX #7)
White Queen (Pheonix powered) beats Sentinel (Juston Seyfort) (Avengers Academy #33)
White Queen (Pheonix powered [P5]) beats Thor (AvX Versus #4)
Stalemates:
Beast vs. Iceman (Wolverine and the X-Men #12)
Captain America vs. Rachel Summers (Wolverine and the X-Men #12)
Captain America vs. Wolverine (AvX #3)
Daredevil vs. Psylocke (AvX Versus #4)
Gladiator vs. Cyclops (Pheonix powered [P5]) (Wolverine and the X-Men #13)
Hope (Channeling Shao Lao) beats Cyclops (Pheonix powered [P2]) (AvX #10)
Magik (Pheonix powered [P4]) vs. Colossus (Pheonix powered [P4]) *Double KO
Moon Knight vs. Gambit (X-Men Legacy #267)
Rulk vs Colossnaut (AvX Versus #3)
Rulk vs. Iceman (Wolverine and the X-Men #10 & 11)
Thing vs Namor (Uncanny X-Men #12)
Thor vs. Rachel Summers (Wolverine and the X-Men #12)
Warbird vs. White Queen (Pheonix powered [P5]) (Wolverine and the X-Men #13) *Warbird is escorted away by Gladiator
Other fights:
Captain Marvel (Pheonix powered) beats Thor (????)
Cyttorak beats Colossus (Pheonix powered) (Uncanny X-Men #15)
Dangers beats Pixie (Uncanny X-Men #13)
Dangers beats Primal (Uncanny X-Men #13)
Dangers beats Transonic (Uncanny X-Men #13)
Dangers beats Velocidad (Uncanny X-Men #13)
Madelyne Pryor (3 clones) beats Cyclops (Pheonix powered [P5]) (Uncanny X-men #16)
Madelyne Pryor (3+ clones) beats Magik & Colossus (Pheonix powered [P5]) (Uncanny X-men #16)
Madelyne Pryor (six clones) beats Namor (Pheonix powered [P5]) (Uncanny X-men #16)
Madelyne Pryor (unknown number of clones) beats White Queen (Pheonix powered [P5]) (Uncanny X-men #16)
Professor X beats Angel, Beast, Captain America, Giant Man, Ice Man, Kid Gladiator, Namor (Pheonix powered [P5]), Quicksilver, Racheal Summers, Thor, War Machine, Wolverine
Sebastian Shaw beats Hercules (Avengers Academy #30) *Mortal form
Sebastian Shaw beats Madison Jeffries/Box (Avengers Academy #30)
Sebastian Shaw beats Tigress (Avengers Academy #30)
Shao Lao (Adult) beats Pheonix (Full) (AvX #10) *Mentioned
Warbird beats Iceman (Wolverine and the X-Men #13)
Only fights that are conclusive (or one person shows a clear advantage) or have some substance (Rather then just one panel and not shown again) is mentioned in the above list.