One important variable is bar speed. If you read Louie Simmons he says that percentages, sets, and reps are just guidelines to help adjust bar speed.
Heavy, low reps sets move slowly, and build strength. You literally cannot do many reps before you fail. So do singles or low reps for several sets to get "quality" work in.
Medium weights, move quicker, and build power. Do Low reps and many sets to "practice."
Low weights mean less force, so you do many reps. This leads to more TUT, "pumps" and hypertrophy.
I think this is why the Bill Star 5x5 workout is so superior to Starting Strength or Stronglifts where you lift the same weights over and over. Using different weights in your training, even doing the same lifts, allows for so different bar speeds and so much more variety.
The Juggernaut scheme does look like 5/3/1, just with numbers to guide you instead of percentages. 10's or 70%, 8's at 75%, 5's at 80%, 3's at 85%. You lift deifferent weights, which leads to different bar speeds and time under tension.
Most of the rep/set ranges you mentioned (8x3, 5x3) are pretty close to each other. Experiment with radically different schemes and you can really "feel" the difference. Try...
2 sets of 15 reps with a 2 count pause at the top and the bottom around 50%.
6 sets of 3 reps with 80%, moving the bar as forcefully and quickly as possible.
3 singles with 95%+
This will give you a better frame of reference.