The 870 is far and away a better weapon if abuse and/or extended use is possible. I am not guessing on this, I was an armorer in the military and during my tour the 870 was phased out and the 590 and then the 590A1 was coming in. I can break a Mossy in less than 25 strokes with the 500 mossy giving up in less than 5 strokes usually (please bear in mind that what I do to accomplish this is pure and simple abuse aimed at breaking the weapon) and cannot break the 870 in one session. The 870 WILL have the same failure from the same abuse, but will take over 100 cycles to do it. The Mossy is a GOOD shotgun!!! It is a solid gun in 99.9% of uses, but it is not better or equal to an 870.
The heat shields do work, and do not cause any problems. If you shoot a lot get one, well worth it. As far as pistolgrips go they only have one place, and that is on a folding stock gun. Folding stocks are only suitable for CQB/entry guns IMO. On fixed stock guns pistolgrips front and/or rear are cumbersome and accentuate recoil IMO. Speed on target suffers for me with a pistolgrip, and I have many thousands of rounds with them on.
Stay very light on accessories, VERY few are beneficial. The sock on the stock for shells is THE WORST ever on a defensive gun. Say your cover provides well for left handed shooting and you are righthanded, the shell sock prevents you from firing the shotgun left handed if on the weapon. You are either exposed to shoot, or get your face mangled and miss with the sock on. If you need extra ammo ON the gun do it on the sling or on a sidesaddle. If you are serious about using your shotgun for defense you shoot at least 25% of your practice with your off hand and one armed right? If you add anything make it an extended magazine tube and quality synthetic stock and forend.
Just my honest opinions from my experiences, hope it helps.