Both are fine shotguns. I own several 870's. I have owned a couple of 1100's and 11-87's.
I am partial to the 870. It is basically the standard that every other pump gun aspires to be.
The 870 is without a doubt the easiest to take down to nothing and clean.
I speak from experience. I started duck and goose hunting with an 870. Salt and fresh water. Other waterfowl hunters will tell you: use them as canoe paddles, dumping them overboard or leaving them in a foot of water, an inch of ice frozen to the entire surface and pull the trigger and rack, still perfect. etc. I have beaten the hell out of several 870's, all keep coming back for more.
As to re load speed: a smooth, well worn, clean 870 can keep up with an 1100. And no gas problems. The difference, with practice, is so minute, the lack of gas problems and take down headaches makes up the .02 % difference in shell extraction and re load.
Can you tell I'm partial to 870"s?
Keep your head down!!!!