At some point in the history of the 870 Police guns, Remington started using heavier springs in certain areas- to include trigger springs. I don't know when that change was first made, my 1989 vintage 870P agency trade-in has a noticeably heavier trigger pull than any of my other 870s.
It could be a simple spring change to a 'non-P' trigger spring (accomplished by a 'smith, this is NOT do-it-yourself territory) will make things feel better. It shouldn't be a huge issue even as is, most folks 'slap' a shotgun trigger and don't worry about having rifle-like crispness. Still, if it feels bad to you it will be an issue in shooting the gun(s) well, so do what you need to do to get it like you want it. I suggest starting out with a good cleaning of the trigger plate assembly with GunScrubber or a non-plastic-damaging spray-on brake cleaner, followed by a good lube job with RemOil or the like. If that and some 'work polishing' doesn't do it, it needs some attention from a gunsmith.
lpl/nc