Welcome to CGN!!
There are LOTS of opinions on this topic! chances are you will be happy with either an 870 or a 590. Both are solid designs and you likely cant go wrong.
Depends what you are going to do with it, but since this is in the tacticool shotgun forum, i will assume it will be for that purpose...
First of all, (in my very humble opinion) avoid the 870 express shotguns, i have one, i am not terribly impressed with the fit and finish, it seems to be a bit of a rust magnet too... at least far moreso than my other firearms...regardless of all that the 870 express tactical is priced well and they seem to be widely available...
I also must admit i have never laid my hands on an 870police, i definitely wish i had held off buying an 870 until an 870p came along. By all indications they are fantastic...
One thing to bare in mind is that the 590/590A1 are cylinder bore, so you can't put in a choke in it for clays or waterfowl or whatever... but really go get a proper gun for that anyhow...
I personally believe that the slide release is in a better location on the mossberg. The location of the safety is somewhat debated... on the mossberg you can see the safety without turning the gun, but the 870 is accessible without moving your finger away from the trigger guard... i like the mossberg safety better but i'm not sure it would work well with a pistol grip, should you go that route. Metal trigger group... i dunno... its good thing but is it necessary? probably not. I would submit it is certainly preferable to plastic...
Consider the 590 with the ghost ring sights... I am pretty sure that a 590A1 with ghost ring sights is cheaper than a 870Police but someone might be able to contradict that. Personally i am a big fan of the 590A1 SPX and i would encourage you to check it out, the LPA ghost ring sights are seriously amazing!... it is a heavy gun and has a long (for me) length of pull, so keep that in mind. But they are exceptionally overbuilt, like a tank. If you can spend the extra cash... why the hell not, it is the kind of gun you can expect to have for "the duration"
Good luck with your purchase!
PS also, if you can find one, check out the Remington 870XCS