The battlemaster subclass will have a bunch of maneuvers that you can trigger on a hit to do a chunk of extra damage along with a rider effect (trip, disarm, taunt, etc). TWF gives you a much higher chance to actually hit and apply that maneuver. Probably not going to give you a superior DPR, since you have limited maneuvers, but you're more likely to hit when it counts, which can make a BIG difference if you're, say, taunting a bad guy off the mage or tripping a scout who would run for reinforcements.