I have a special affinity for the 870 after toting one for a while in lovely SE Asia! In a wet climate and conditions so dirty that you'd just have to experience (and endure) to believe, it never failed to get the job done.
Yes, you can do the same things to the Mossbergs and I knew some guys who carried THEM in combat and were also well-served.
Either will get the job done and both are reliable if handled properly.
Since those days of my ill-spent youth, I acquired an 870 Tactical and have 'tricked it out' with a side-mounted shell holder, Knoxx Stock and Tritium night sights.
A left hand injury (permanent damage) has caused me to forsake it, however, because I just can't be sure than I'M going to perform reliably... especially in an adrenaline-flooded situation!
Enter: The Benelli M-4...WOW! Yes, it IS expensive. But, if you plan to keep whichever gun you buy for many years, the M-4 is well worth the extra $$$.
To my knowledge, it's the first semi-auto shotgun that has been accepted by the US Military. If the USMC thinks it's reliable enough to use in the Sandbox, then it's good enough for me.
I've "tricked it out" as well, including the magazine extender (7+1), larger charging handle, side-mounted shell holder, 3-point sling and Trijicon night sights. It is as beautiful to look at as it is to shoot and, through 1,000+ rounds...so far...not one hiccup or cough. This is a semi-auto you can really trust your life with.
Good luck with whatever decision you make.