It isn't as simple as TBT vs. some other regimen. You have to think about the interaction of your training and your nutrition. When you're in calorie restriction, it is very difficult to recover from any workout that maximizes muscle damage. Muscle damage is good for hypertrophy, but in a cutting phase it's more about hanging on to what you've got.
You want to work your muscles hard but not cross the line into the sort of real damage you want in a hypertrophy phase. Plenty of BCAAs pre-during-and post workout should help with retaining muscle.
As tmoney1 suggests, I get best results with higher rep training in a cutting phase.