RIght now I own a couple 870s and a 500 (though if I can find a 590 here in Eastern NC before I deploy again, I'm going to get one) and it's really up to personal preference.
I like the safety position of the Mosberg better but the plastic button can break so this should (and on mine has been) be replaced with a metal one like those from Brownells. The Remington safety button is metal but in some of the newer models, are the J-safety style that has been known to have problems. Again, this would be something I would replace if it were me.
As for the slide release, the Mossberg has it all over the Remington. It falls right under my middle finger and can be depressed without breaking my firing grip at all. The Remington...not so much.
Short of having a finger like E.T. or some sort of orangatang, you are going to release your firing grip if you are going to depress the slide release.
Smoothness is something the 870 is known for. My Mossberg is today pretty smooth as well but it took a lot of rounds through the action to get it that way. Fortunatley I used mine to shoot blackbirds buying rounds by the case when I didn't have time to reload hulls so smoothing it out didn't take all that long. The forend on mine wobbles as well but I guess it never bothered me and it doesn't effect function at all.
Where I do see a very distinct advantage of the Mossberg is in it's inner workings. When I take a Mossberg apart, both the right and left shell stops come out and go back in with little problem, although it does take a little technique and finesse to do it. If I take the ejector out either for cleaning or replacement, it's a matter of turning a slot screw, no great mystery here.
On the Remington, it's a whole different kettle of fish. In order to replace a shell catch or extractor, it has to be staked in place and there is a finite number of times you are going to do this. I've seen some of the old 870s at work that date back to the early 60's that have had shell catches replaced over the years. Some were replaced so many times that the area of the receiver around the catches had been restaked so many times that they have one or maybe two more restakings left and then you are SOL and the weapon would have to go back to depot as unserviceable.
One other problem I've had with the Remington's design is in the shell lifter. Now both of mine are older Wingmasters with lifters that pre-date the flex tab on the current models. If a shell slips past the shell catch and onto the lifter while the bolt is forward, the gun is tied up in a bad way!
Now you can't open the bolt and the solid lifter won't allow you to push the shell back in so you are going to take the weapon apart in order to get the offending shell off the lifter and get the gun back in operation again. I've had this happen once when I was unloading it and a shell slipped past my fingers onto the lifter tying it up and after getting it out, I modified the lifter by cutting a slot in the lifter so if it happens again (and later it did just that by trying to unload it again the same way) I can use a knife blade or key to push the shell back in. Today, the 870 has a flex-tab lifter. If this problem occurs with the new lifter, simply slamming the pump to the rear tends to clear up this problem. However, the Mossberg doesn't have this problem at all. The lifter rides up against the bolt only dropping down when the pump is to the rear making this problem impossible. Granted, this problem with the Remington never came up while in actual operation but it has never been a problem with the Mossberg either be it while in operation or while unloading it either. Again, I believe this is a very definate advantage of the Mossberg design.
Where the Remington has another advantage over the Mossberg is in the aftermarket parts arena. While I've never been big into the "tacti-cool" parts some folks tack onto their weapons, for those that are, the Remington leads all others bar none in this area. With this comes a lot of folks out there that know how to work on them.
In either case, you aren't going to go wrong with either gun. The Remington is smoother, has more aftermarket parts available and people that are familiar with them while the Mossberg is cheaper, better controls and easier to replace parts in at the owner/operator level. Go with what works for you.