The Mossberg 590 was chosen by the military because they were the only ones who submitted a shotgun for testing. Remington didn't need the contract as they had the LEO and civilian market pretty tied up.
It should be noted that the military sent the first 590 prototype back for changes, because the first one didn't meet their specs. It was based on the 500 model.
The Mossberg is a decent gun, but it isn't nearly as good as some are making it out to be. The plastic safety tends to fail a lot, and that's usually the first piece replaced. The fit and finish isn't all that great, even compared to an 870 express. They are fairly reliable, though, if you don't count the safety.
I would say that the 870 is a better shotgun, though. Better fit and finish, and a slightly more solid design. That includes the Express line. You pay for the more solid design in weight, though. It is not a light gun, mostly due to the steel reciever vs. the aluminum one on the Mossberg.
The placement of the controls is slightly more convenient on the Mossberg, but with practice the 870's controls are very easy to get used to.
I have an 870 express, and the only real complaint I have about it is the blueing. They bead-blast the blueing to finish it, rather than the polishing they give to their Wingmaster's series. It makes for a fairly rough texture, and it tends to pick up dirt and grit a little too easily. Other than that it has worked flawlessly since I got it. I haven't had any rusting problems, either, and I don't baby my guns.