PPP tapers down to mainly singles about 8 weeks in.
I really enjoyed it, having to do set weights really makes you focus.The down side was, for me personally, if i worked shift work/sleep/social activities and wasn't 90-100% towards the 1rm's it was very hard and not forgiving, which isn't a bad thing, I just found I wasn't up the task.
Progress was very successful, just the same. From a torn hamstring and not walking properly for 3-4months, to an increase of 40/25/35kg in 2-3 cycles of it, just one deadlift cycle as I did a lot of SLDL to get some hamstring strength again.
5/3/1 on the other hand progresses based on personal performance and submaximal training. so your 1+ day, bam, 3reps and thats what you calculate your next months totals on. More forgiving I feel in that aspect. Having a rough week, as long as you still hit prescribed numbers as a minimum, you're still progressing.
Only reason I changed from PPP is beacuse I wanted more volume in my main lifts. I was getting to a stage where I was grinding out some reps, which for me personally, isn't how I like to get PR's. If it's not explosive and on point, I don't count it.
Edit: One thing I have noticed with programs is that they are a lot better written, imo, than they used to be, for the public.
Including mobility work etc, and specific conditioning work. Brandon Lilly, CWS, Wendler all have it more in depth in the updated versions of their methods. They all focus on the same thing, becoming strong, all the time.