I don't see how you can be dealing similar amounts of damage with the Dex-based monk. I'm curious! A player in my campaign is currently a 5th level fighter/4th warforged juggernaught, and has nice stats (however, a warforged does not have +2 str, and the juggernaught only has 3/4bab, so this is by no means a maximal damage build; he clearly chose if for the flavor and optimized around it). So this real-life, not super-maximized build currently has 22 str (he rolled high on str and has a strength boosting item and all level-ups in strength), +8 bab, and weapon focus/specialization/PHB2 mastery, and of course, power attack.
He attacks +19/+14 dealing 3d6+15 damage, without special circumstances, using a +2 weapon. It's large (since he has the strongarm bracers), hence the 3d6. +6 str bonus means +9 to damage, +2 from wp. spc., +2 from wp. mastery, +2 from the weapon. His to hit is +19, since that's +8bab + 6 str, +1wp.focus, +2 wp. mastery, +2 weapon. If his opponent has a low AC, his power attack is absolutely devastating. All this is fairly normal stuff, with the exception of the strongarm bracers allowing him to wield a larger weapon.
He has a bunch of bonuses while charging, so potentially his damage output is much much higher, but for the basics, that's enough. And this guy isn't even maximized, having a bunch of flavorful things like a weapon of vanishing, charge related stuff, bull rush related stuff, DR 2/adamantine (at the cost of feats) and the warforged juggernaught class - a plain fighter/barbarian would have +1 bab and up to 6 strength more (half-orc+rage) - not to mention that he could have chosen to focus his feats a little more. He gets up to another +3 to hit and 1d8+4 to damage while charging.
How the heck is a dex-based monk doing anywhere near 25.5 damage at +19 bab on a hit? Let alone how he's competing once power attack and the charge effects are factored in...
A monk at 9th level could have a monk's belt, superior unarmed strike, improved natural attack, and deal 3d8 damage per hit. If he's nice to the druid, he gets greater magic fang for free - 3d8+2. He's got a +6 attack bonus, weapon focus (presumably), gr. magic fang, 26 dex (18+2racial+2levelup+4item) - +17 (3d8+2) i.e. dealing 15.5 damage at +17 instead of +19 attack bonus. And before you say "but a monk has other nice bonuses" don't forget this other warforged isn't a pure fighter either, and has nice immunities to sleep, doesn't need to breathe, is immune to all mind-affecting effects, and is immune to all necromancy and death effects - and maybe more, I don't remember - a true fighter would not have these, and deal significantly more damage, at significantly higher attack bonus.
The because of power attack, the damage issue because very difficult to close.
Since you only get a full-attack if you hardly move, that first attack is the most important. Especially to a monk, who's so good at moving.
So, I'm honestly curious how a dex-based monk can compare to a more normal fighter type, especially a barbarian, in terms of damage - I just don't see how!