Tough call, but since I have Les Pauls with each of those pups in them I guess I should give it a shot... First I have to say that I like both quite a bit. However, here's what I notice about each...
The Duncan Pearly Gates are a great classic rock pickup. I love them. There is a slightly increased mid-range response over a standard PAF pup, and this is even more noticeable in comparison to the BB Pros in my other LP. I have used the Duncan '59 quite a bit also, and I like the extra mids in the Pearlys better. Gain wise they are similar to most PAF type pickups.
The BurstBucker Pros in my other LP have noticeably less mid-range than the Pearlys. They are smooth, but have a bit more treble bite. Initially, I didn't like them and preferred the other guitar with the Pearlys, but they have really grown on me over time.
The verdict... (sort of)... generally I grab the LP with the Pearly Gates pups for a rock sound and the LP with the BurstBucker Pros for a purer blues tone, but they both sound great on almost anything. I have vids of each guitar here - the gold top has the Pearlys and the faded has the Burst Bucker Pros. However, I used different guitars with different amps on different songs, so there is no direct comparison - sorry.
Hope that is helpful. Hit me back if I can be more illustrative.