You don't need to do just one of the two. You CAN do high reps for some exercises and low reps for others. The thing is that with the programming of SS model, because you are hitting almost all lifts or their variations 3x a week, you can't have much variation in the set-rep scheme without adversely affecting recovery.
HOWEVER, you could simply change up your SS model a bit and add in a few things which you might find beneficial.
I know from personal experience that I would simply HATE to do squats, deads or bench press above 3 reps lol...But, if I am going to be doing push-ups, dumbbell presses, lunges, etc I want to keep the reps higher because I am not training those lifts to maximum capacity in terms of absolute strength.
SO, lets say you want to switch things over (and this is all assuming that you aren't progressing - I am totally in favor of what HITHopper has advocated in his posts earlier), this is one way you could make changes:
Pull-ups 5 sets to failure
Standing Unilateral Shoulder Press 3x8-12
Cable Rows 2-3 sets of 10-12 reps
Unilateral Box Squats (do some practice here because the end goal is to be able to do them without a box aka Pistol Squats)
Glute Ham Raises 3-4 sets of 6-10 reps
Flat Bench Press 5x3
Low Incline Dumbbell Bench Press 3x8-12
Chin-ups 4-5 sets to failure
Overhead Squats 2-3 sets of 3-4 reps
Front Squats 5x3
Back Squats 2-3 sets of 5-6 reps depending on how you feel
Dumbbell Rows 3-4 sets of 8-12 reps
Push-ups 5-10 sets of 10+ reps depending on how you feel
This is basically it. You don't even need to do back squats on Friday because IMO OH Squats and Front Squats put together kick Back Squats out of the court
With these changes you are getting QUALITY
work done - and that is the key factor: not how many reps you are doing or which exercises but QUALITY of what you are doing to achieve your goals of losing weight and getting strong.
If you want to lose weight buy Leigh Peele's Fat Loss Troubleshooter. I got the link in my sig. It's probably the best $70 you'll ever spend. If you don't click on the link in my sig you're gonna get banned....(j/k..not quite ;) )