It's not either-or. Low-rep (1-5) high weight is for strength. High-rep (8-12) with lower weight is for muscle endurance, but we would never suggest more than 10 reps for any powerlift set.
A typical powerlift sequence is a warm up set with very light weight, then 4-5 working sets advancing to your day's target. For example, lately I have been doing, say, with deadlift (most important exercise, I feel), warm-up set of 5 at about 100, 5 reps at 155, 5 reps at about 180, 1 rep at 200 and another rep around 225. Like I say, I am not a big strong guy. Everybody is different. My one-rep max is probably 245, but I don;t know for sure. My goal is 300.
Many fitness people do a week of high rep every month or two. "Lower weight" is around 60-70% of your one rep max. "Higher weight" is around 80-90% of your one rep max.
As always, there are exceptions, mainly for accessory exercises. For example, for curls or tricep cable push-downs, 10-20 is fine to keep those things "toned".
My take on heavy weights: Pull-ups are heavy weight. Push-ups are just calisthenics. If you can do 20 pullups bravo to you and put some weights on you to be more efficient. I won't do barbell bench or barbell squats without trainer or partner. Without those, I'll do dumbbell bench and kettlebell lunges or squats instead. If no weight station is free, I'll do kettlebell deadlifts or trap bar instead of regular. It's all good as long as it is HARD and makes you want to cry or spout 4-letter words.
Since I only do half of my powerlifts one day, and half of them another day (not ideal for strength but ok for fitness), I fill in my weights hours with accessory lifts to get a full workout. But to be more precise, I also do pullups twice/wk and one day of dumbell bench and another day barbell bench because I want to focus on those right now. There's only so much time to fit in weights, calis, and plain cardio. If a week had 8 days, I'd do another day of weights. It doesn't fatigue you like calis, but it kicks your ass and kicks your mind.
