For me personally, I stick mostly to the same grip - on the valve casing with left thumb working the 1st valve slide and middle finger working the 3rd. Lower 2 fingers are wrapped around the valve casing below the 3rd slide. Occasionally I'll deviate from that but I conciously try and keep it the same as I do with so many elements of playing; if I keep as many the same as possible, it makes it easier for me to realise what might be "out of whack" if things aren't feeling right.

I would contest that the thing that may be altered most by shifting your grip is not the angle of the horn so much as the angle at which pressure is applied to your chops. Thoughts and opinions?