Two weeks ago I rode a TT, for the first time in possibly ten years ! So my opinion is very personal, but here goes.
I remember riding TT's and edging hard with the kite quite forward in the wind window, and doing this I got upwind reasonably well, but my aim at that time riding a TT wasn't to get outside the Break to hunt down another good wave. but just to tack back upwind after jumps, playing, practicing.
I find Surfboards a total different story, usually they point quite high, and go up wind well. the best one I had (I still own it) is a 5'4 Quad fin, fairly narrow, slightly heavy, dart !! it goes up wind like it's on rails, using a combination of keeping a good length of rail engaged and two of the back fins engaged, so basically using the rail and fins, ( forget that "riding it off the fins" rubbish !) keep the nose down, so you engage more rail.
The Mitu 5'8 is obviously a thruster three fin set up, not theoretically as good upwind as a quad, but has fairly straight rails in the mid section, and at 5'8, it's rail length helps. I never have any problem getting upwind quickly with the Mitu,
I often see TT riders in the waves at some beaches, so they obviously get out there. but I think the surfboard gets there quicker.
Hope that helps.