Unless I misunderstood your question, I think you're asking whether you should do the 10-minute intense workout or the 20-minute moderate one, right? I'll answer that question (and if I'm wrong about your question, "sorry!" in advance). I think it depends on what you like. I tend to like shorter, intense workouts, but sometimes I'm not in the mood for that, and I do a longer moderate workout. Go by your energy level. You could also try alternating them, i.e., do the 10-minute intense workout one day, and do the 20-minute moderate workout the next. This would also give you some needed variety.
I admire the fact that you're still managing to fit workouts into your schedule while working two jobs. But as the others advised, don't skimp on your sleep. I've seen studies that show that people who do not get enough sleep tend to be more overweight than those who do get enough sleep.
Edited to add: If it's any help to you, I've found that when losing weight, food is 90% of the equation (i.e., rather than exercise). When I was in my 20's, I didn't know squat about exercise, but I still managed to get to the lowest weight of my adult life just doing a 15-minute Jane Fonda workout in the a.m. It was a lame combination of some jumping around for cardio and then some floor work exercises (leg lifts, etc.). I did that short workout every day, and I was toned and thin. Now, maybe it had something to do with the fact that I was in my 20's
, but I think most of it had to do with the fact that I was stringent with my eating.