I've played around with both personally. If I'm cutting, I actually do it both, before AND after. Only very shortly before, around 15 minutes, pretty light intensity, not breathing hard or anything, just work up a little sweat, burn some calories, get the heart rate elevated just a bit.
THEN I do my workout, and then I hit the HIIT hard for 30 plus minutes afterwards.
Maybe my workouts suffer a bit, if I had to put a percentage on it then maybe like 10 percent I would say. But you know, when i'm cutting, setting new PR's in lifts isn't really on the agenda.