IMO, it sounds "vintage good" like an older P bass, warm and smooth.
It's not a loud, edgy pickup (neither is the Area J) but I really like both.
I think the Dimarzio description is accurate:
"This set is the complete package, teaming up the Area P Pickup with the Area J Pickup.
The DP250 Area P 4-string Pickup from DiMarzio has everything you're looking for in a great vintage sound. It's a nice warm tone with awesome sustain.
With the Area J you get a pickup that has a precise attack, with a tone that hits in the center. It has clean, clear lows and silky, open highs.
The Area J Bridge pickup is designed to fit the original Fender Jazz Bass, which has different sized cavities for the bridge and neck pickups. Make sure to reference the dimensions of your bass when making your selection.
It has reduced pull thanks to its' Alnico II Magnets, which you can wire in either series or parallel humbucking depending on what you're looking for."
I have used a Seymour Duncan SPB-1 Vintage P with STK-J2 Hot Stack J bridge in 2 other PJ basses, and that combo sounds great as well.
To me, the SD Vintage P sounds like a "new" vintage P pickup would sound, where the Dimarzio Area P sounds more "used".
The Dimarzio Area J sounds more like an older single coil than the SD Hot Stack, but I'm a fan of both.
I've always used 500k volume pots and Fender TBX tone control with the SD PJ pickups I mentioned, and I'm sure that has some influence on the tones.
I have never used the EMG Geezer pickups, but they seem to have many fans lately as well.