For what it is worth, I know people who are on 5/3/1 and are strong but not big. I think it comes down to the assistance lifts. Ill give you a direct example of what I just got done doing (will be switching my routine since my schedule is changing)
(Upper Body Days)
Assistance 1 - 3 sets of as many reps as possible with a lift similar or identical to the 5/3/1 lift. The goal for this lift is to get 20 reps on the first set.
Assistance 2 - Antagonist movement to 5/3/1, heavier but reps for AMAP, 3-4 sets. My goal is 10 reps for the first set.
Extras - depending on how I feel or what need improvement, something simple like triceps, shoulder, biceps, etc
Cardio - Stationary Bike, Running, 100 air squats, anything fun that gets the heart beating.
(Lower Body Days)
Assistance lift - 3 sets of AMAP reps, the goal here is 10. This lift is also similar to the 5/3/1 lift.
Weighted Carry - 3 sets for max distance. The weight depends on how my back feels.
Extras - good mornings, lunges (rarely), SLDS, anything that needs work.
Now, I cant explain why, but I have big legs, big torso, and A big yoke (small arms though) and don't follow any sort of size building routine. All I do know is that this has worked for me pretty well. I feel the common denominator is using assistance lifts that can be hit for at least 10 reps and are done to failure. I have certainly seen my recovery improve between strength sets by doing these lifts. My diet is mediocre, but mostly consists of protein and fats, and very little carbs.