Ranger's do out DPS barbarians on a favored enemy, but only IF:
They have the same to hit versus their enemies AC then the barbarian. (this is not the case most of the time)
They have power attack (not all rangers take it).
Basically Gunga, what i'm saying is that most of the rangers you run into are probably not pimped as much as your barbarian - They probably don't have enough to hit to be able to hit every mob on a 2 or more. If they don't, then there will be a huge difference between you hitting 95% of the time and them hitting 75% of the time. I guarantee that if you would consistently run with a Ranger that has the same gear and the same weapon you have against a favored enemy, you'd loose out. Given of course both are dual wielding DPS weapons. Seriously, the ideal way to compare is to run the math, but this has to include to hit with bonuses versus mob AC.
BTW, Rangers vs Barbarians, there's usually a net 4 points of to hit difference. Rangers being 32 str, Barbarian being 40 and most rangers having taken a Monk level and or rogue level for 2 more bab while taking a +2 to hit from enhancements versus their favored enemy. That can have a huge effect depending on what the AC of the mob is and when you can turn on Power Attack or turn it off (that is if the ranger even has it).