Give me a default AC and I'll get you an answer.
Lets say that we have some feats involved. Our level 1 Avenger is using an Executioner's Axe, because he listened to me and went for high damage and high criticals.

Our level 1 Ranger is using twin Bastard Swords. Both have 18 strength. Both are fighting a monster with AC 15. The Ranger is using Twin Strike, and the Avenger is using something that doesn't have an effect on accuracy or damage (either one of the previewed at wills will not modify expected damage, though they do provide positioning benefits).
The Ranger has +7 attack, will deal 1d10 on a hit, and +1d6 if he hits at least once. He gets two attacks.
The Avenger has +6 attack, will deal 1d12+4, Brutal 2, High Crit on a hit, and he gets to pick the better of two attack rolls.
The Ranger's expected damage, ignoring criticals, is .65*5.5 + .65*5.5 + (1-.35*.35)*3.5 = 3.575 + 3.575 + 3.07125 = 10.22125. He also could have attacked two enemies with this at will, if he chose.
The Avenger's expected damage, ignoring criticals, is (1-.4*.4)*11.5 = 9.66. He also gets some positioning advantage.
Lets say we add in critical hits... give me a moment and I'll edit...
The Ranger's expected damage, including criticals, is .6*5.5 + .6*5.5 + .05*10 + .05*10 + (1-.4*.4)*3.5 + (1-.95*.95)*6 = 3.3 + 3.3 + .5 + .5 + 2.94 + .585 = 11.125
The Avenger's expected damage, including criticals, is (1-.45*.45)*11.5 + (1-.95*.95)*19 = 9.17125 + 1.8525 = 11.02375.
Darn close, actually. Right now the Ranger has more opportunity to boost his damage (weapon focus works twice for him, once per sword, and he can boost the die of his quarry damage), but who knows what the Avenger gets for feats.
The Ranger is another class that rewards critical hits, for the record. Since bonus dice are maximized, and since it gets two attack rolls.