I own an 870 and a 500 Mossberg, so lets talk about pump guns.
Each has certain advantages.
Both are reliable like a brick wall.
I find the 870 is better balanced and the action is the slicker of the two.
I also prefer the 870's safety, being more tactile.
Mossberg's have dual extractors rather than the 870's one. While both guns extract reliably, the Mossberg's redundancy could save your bacon one day. Moreover, the extractor on the 870 is brazed to the inside of the receiver. If it ever breaks, it means a trip to the gunsmith and no small amount of $$ to fix it. Mossberg's extractors are retained by screws. If one breaks you can change it at your kitchen table for a few bucks and 10 minutes of your time.
So, if reliability is a prime consideration, I'd select the Mossberg. If smooth function and great balance are a big factor, go with the 870.
Both manufacturers have budget shotgun lines that cost less, but are no less reliable. Maverick is Mossberg's budget brand, while Harrington & Richardson (H&R) is Remington's low cost entry shotgun.
I owned a Maverick years ago and it was a great home security shotgun. I gave it to my sister's husband and replaced it with an H&R Pardner Protector. This is a dedicated security shotgun, that is a literal clone of the 870 action, with a slightly re-shaped receiver. All 870 accessories fit it. Barrels, however, are NOT interchangeable. Around $200. It weighs about 1/2 pound more than the 870 as it has a beefier action and thicker-walled receiver. 18.5" barrel, black nylon furniture with sling swivels. Holds 5 in the magazine, plus 1 in the chamber. Parkerized finish.
Ultimately, all the above will do what you need. There are no bad choices here.
Edit to add photo of my H&R....
