Other than both being done with a barbell, I think they are pretty different programs, really. Here's how I see them in a nutshell.
PTTP. Super minimal. Focus on two movements. Get good by doing them many times a week (4-5). The focus is on strength over size, unless you are following the Bear protocol.
5/3/1. Not a minimalist program. Get strong on the four main barbell lifts through highly structured periodization. Lift 4 days a week but only do each main lift once a week. A little more balanced than PTTP as you focus on a big pull, big squat, vertical press, and horizontal press. The focus is on strength with a bit of hypertophy in there (more than PTTP do to warm up, reps, and accessory work). Could be a pure hypertrophy program if doing the Boring But Big option.
I'd say run the one you're most attracted to. Stick with it for many months and then try the other one. Due to the cycling and infrequent use of each lift, many people stay on 5/3/1 for years and have success. I don't believe many people are capable of doing that with PTTP. Once the weights get heavy you need a different program.