Generally, out of the box, the Police will have a smoother action, as they are finished a little better. This can easily be remedied with 0000 steel wool and shooting, over time: no big deal to me, although others may differ on how important this is to them.
These are the ONLY internal parts that are different between the Express and the Police:
1. The trigger housing on the Police is pressed metal, that on the Express is polymer - advantage Express, as the polymer trigger housing is known to be more durable (ask any Remington armorer). I have bent a few Police guards, but have never damaged an Express guard. Note: I have recently learned that the newer P guns are now also using the polymer trigger guards.
2. The extractor on the Police is forged, the Express is MIM. Upgrade the extractor:
http://www.brownells.com/.aspx/pid=10745/Product/EXTRACTORCost $14.99 (I always replace the extractor, but have never seen a MIM extractor break on an Express).
3. The Police has a stronger carrier dog follower spring than the Express. This is also an easily upgrade:
http://www.brownells.com/.aspx/pid=10763/Product/CARRIER-LATCH-SPRING It is listed as a carrier latch spring for the 1100 and 11-87, but this is the correct spring used in the Police. Cost $4.84 The interesting thing is that Remington charges the same for either spring (the P is black, and that is the only way to tell them apart). So why not use the same spring in both guns? Marketing.
4. The Police uses a stronger magazine spring on the 6+1 versions (I believe that both 4+1 versions now use the same spring). Purchase a new spring from Wolff:
http://www.gunsprings.com/Rifles%20%26%20Shotguns/REMINGTON/870,%20878,%2011-48,%20SPT-48,%20SPT-58/cID2/mID108/dID216#606 $8.99
5. Sear spring - As of several years ago both versions now use the identical spring (the one from the Express).
Those are the only differences that matter between the Express and the Police; the rest is simply marketing. Most of the custom 870 builders, such as Wilson Combat, Nighthawk, and AI&P Tactical use the 870 Express platform because it is basically the same gun at a lower cost.