I've tried both, and I definitely understand your dilemma.
My vote is Tahm.
There's just something about yanking your allies out of enemy CC, or getting them back to safety when they're low health that's an awesome feeling. Admittedly, every once in a while you'll mess up, eat the wrong target or yank someone out when they thought they could get a kill, but the general feedback I've gotten from teammates has been incredibly positive. You also can defend your base fairly effectively, devouring Super Minions spitting them back out at the wave, and repeating over and over.
Bard's mistakes feel more costly, while his successes feel standard. Everyone expects you to ult the enemies that are getting away, buying your team time to get there to finish them off. There's not many "good job"'s for that. There are a lot of "way to go bard" when you think "I've got to stop the enemy from getting to us" right as someone your team thinks "Now's a great time to use my ultimate!"
I'd say if you like supporting the team, pealing for people, and denying the enemy team, Tahm's the right champion for the job.