Okay, here's my take on it.
Remington 870: Excellent reputation with the law enforcement community as a dependable shotgun. Several places available to hop it up a little or a lot, depending on what you want from it. Considered by many to be the ol' standby. I don't think you could go wrong with one.
Mossberg: My personal choice. In my opinion, the controls are placed better. I have a 500, 590, 590A1, and an 835. I have yet to see ANY failures of any kind, even with the wide variety of shells and slugs I make them digest. The military also has had several contracts with them (so they had to pass the MilSpec testing) resulting in the 500-mil and the 590-A1. The 835 is their "sportsmans" model with the longer barrels and screw-in chokes.
Winchester: I have heard from several folks that think their Defenders are the best thing since sliced bread, but I've had no experience personally with them, so not a lot to say.
Maverick: It's been a while since I've seen one, but if I remember right, the design is exactly the same as the Mossberg. I believe Maverick is an overseas division of Mossberg, or at least partly owned by them. I could be wrong on this. What I don know for sure is that they are, for all practical purposes, a mossberg. The prices are lower, but in my opinion, it's not a worthwhile trade off.
My recommendation, for home defence/SHTF/etc, buy a Mossberg 590-A1. For ducks/trap/skeet/etc. look into a Mossberg 835 Ultimag or a Remington 870 Express or Wingmaster. I don't doubt that the Winchester is a fine arm, but I can't recommend them myself due to lack of information on my part. I hope this helps some.