The 870P Police is the Cadillac, the Tactical is the Chevy the Mossberg 590A1 is a plain Chevy.
The Mossberg has a cast aluminum receiver and stamped internal parts.
The 870 is a forged steel receiver with heavy-duty fabricated internal parts.
Both brands are durable guns, but the 870 is more so.
The Police is more polished inside and out to remove all machine marks and burrs.
It's smoother out of the box.
It gets more inspection and hand hand fitting to insure reliable operation for use in police situations.
It has a parkerized or blue finish and comes with a wide range of configurations.
It has a milled extractor, a heavier carrier dog (lifter) spring to insure correct feeding under the recoil of heavy shells, a heavier trigger-sear spring to prevent accidental discharge, and on the 4 shot magazine models a heavier magazine spring, again to make sure the gun feeds properly under recoil.
The Police trigger guard assembly is made of powdered, compressed aluminum.
The Tactical is a dressed up Express gun.
It has machine marks and some burrs left inside and out.
It's a little rougher out of the box, but smooths up with use.
The Tactical guns have various "painted" type coatings. These are reasonably durable, but do scratch and scrape.
The extractor is MIM, it has standard Express springs.
The extended magazine versions have the same spring as the extended magazine Police guns.
The bore and chamber are not as well polished as the Police. It can be polished with 0000 steel wool on a used bore brush and an electric drill.
The Tactical trigger guard assembly is plastic. This may be better then the powdered aluminum unit.
Going on the basis that I've never said, "Gee, if ONLY I'd bought the cheaper gun", I recommend the Police if you can afford it.