Yes, they'll have a different texture. That said, the look of Tri-X in medium format and larger is classic. Tri-X/PMK is my B&W combo of choice for medium format, Tri-X/Acufine for more speed. Delta 400 is really nice in Perceptol at EI 200 in medium format, or EI 400 in D-76 for a little more grain, but an extra stop.
I'd say, if you want to go handheld, take advantage of the speed and go with a faster film.