At Xtreme Couture, it depended upon the instructor...
Kui was more about building mental toughness and conditioning, his classes are very high paced and have a lot of intense partner drills (like non-stop knees on a partner holding a medicine ball, which is painful and draining for both guys), hard bag work, intense rounds on the pads, etc.
Kampmann focused on buildin up muscle memory & reaction time, as well as good technical form. Lots of partner drills for throwing, slipping & blocking combos; an emphasis on footwork and solid fundamentals, and methodical sparring (with a focus on having good form).
Joey Vanier (who isn't at XC anymore) was my favorite- he really delved into the strategy & psychology of kickboxing, the chess match. He really advocated the "kick the puncher, punch the kicker" strategy, and emphasized having a rounded & polished skillset so that you could have a strategic answer for any stylistic problem. He also emphasized solid fundamentals and mental toughness, we'd do partner drills jamming & checking leg kicks, and would then do partner sparring with limited rules (IE one guy can only kick while the other punches, you can only strike with your left or right arm and/ or leg, etc) which really helped me with my body awareness, and forced you to develop individual weapons and timing.