Mining guy here. It 95% cost. TBM is great if you have money and are going through residential type areas, can get through most rock, not as nimble though.
Drill and blast are the most common by far, especially in mining industry where they are lots of twists and turns, and no-one cares about noise etc.
Channel tunnel was extremely soft and in places wet ground, mostly chalk. Comparatively quick to bore through. Blasting would have either wrecked the ground structure in too large an area or gone "splat" instead of "bang".
Drill and blast are the most common by far, especially in mining industry where they are lots of twists and turns, and no-one cares about noise etc.