I tried Ilford Delta 3200 shot at 1600, Tri-X400 pushed to 1600, and Tmax400 pushed to 1600 all in one scene within 2 hour period. When printed, they were amazingly similar in tonality, grain, and overall look. I'd say just pick one and start shooting.
I'm sure there are lots of technical differences among those films I used. I just didn't see any that mattered enough.