There has always been a rivalry between the Remington 870 and the Mossberg 500/590. Both are robust platforms that are dependable. However, most people prefer one over the other. I would challenge anyone who is about to buy their first shotgun to handle both.
Most will typically find the Mossberg to be a tad less expensive and lighter weight. However, you will find far more after market accessories for the Remington than the Mossberg.
You will also find the maintenance, disassembly, and assembly far easier for the Remington than the Mossy. I have found that several of my former students that have taken my shotgun classes, have never thoroughly cleaned their shotgun. Most advise that if they would have realized the difference in the way the two shotguns were designed, they would have chosen the Remington.
There are some that will argue that the Mossberg‘s controls are more user friendly; like an ambidextrous safety. I guess you need to ask if this is the major reason for buying the shotgun. Everyone in my family is right handed. Even if they weren’t, this is not my only defensive weapon. You also need to break your firing grip to reach the safety on your Mossberg unless you have incredibly large hands. I do not need to break my firing grip to disengage my safety on my Remington 870.
Some might also argue that the action bar release can be reached with the firing hand without breaking your grip on the Mossy. You will definitely have to break your grip with the Remington. However, when you consider that you typically use this in an administrative manor 99% of the time, it is really not a deal breaker.
This is just my two cents. Please feel free to reply.