The 11-87 is supposed to be the improved version of the 1100.
It has a self-compensating gas system, stainless steel magazine
tube, improved extractor plus other up-grades I can't recall.
The most desirable trap version would be the 1100 Competition
I have left handed versions of both. I do like the stainless magazine tube on the 1187. Other than that it is pretty much a toss up for me. I suppose I might give the 1100 a slight edge because I was able to find a 30" Rem choke barrel for it. Apparently Remington never made a 30" barrel other than the trap style for the 1187.
I have and shoot both. Each has its own distinctive shooting characteristics.
Properly maintained, each will last forever allowing that you will need to periodically replace a few parts.
I am partial to stepped rib barrels and fixed full chokes.
Shoot each and then decide which works best for you.
If you want a "games" gun in trap configuration and want to shoot more than 3 1/4 DE and 1 1/4 oz. of shot, then you need the 1100. The 11/87 trap model is not pressure compensated and is not designed for the big stuff.
You're being really vague, because both fill their own niches.
Overall, the 1187 is an improved 1100, because it has a gas compensating system that allows both light 2-3/4" shells up to heavy 3" 2 oz loads, buckshot and slugs to be shot from the same barrel. This means you do not need to have extra barrels, like the 1100 would require.
If you're talking about trap guns, the 1100 and 1187 were both made for trap. Frankly, there's not a lot of difference, because the 1187 trap models lack the gas compensating system. Late model 1100 trap guns actually use the 1187 bolt. It comes down to preference for features on the guns, since both have had option changes over the years. The "best" trap barrels are considered to be the fixed full choke factory backbored 1100 barrels, and the 1187 factory backbored, step rib barrel with choke tubes. The late model 1100 trap is, frankly, rather plain for options. It has a flat rib barrel, not back bored, but does use choke tubes. Early 1100s were glass smooth, as are early 1187s. Machining got rougher in the late 1990s.
Pretty much the same advice applies to skeet and sporting clays. Both the 1100 and 1187 were made in these configurations. The 1187, though, was made in a special sporting clays version with a shorter forend (though the "barrel hanger" is in the same location so no special barrels are needed).
I have several 1100s and 1187s. A trap gun of each, a 20ga 1187 set up for sporting clays (and trap), and several hunting 1187s. My son has a 12ga 1187 and a 20ga 1100. My daughter has a 20ga 1187. Obviously we like them. For mine, I installed monte carlo stocks on all of them, including the camo models, so the point of impact matched my trap guns. Just made it more natural for hunting.
I also own and shoot both. My Remingtons are field guns. I think it's pretty much a toss up also but, the 11-87 will handle 3" and has the choke tube changeability. I was lucky enough over the years to pick up a 30" fixed full and a 26" sheet barrel for the old 1100 which came factory with a 28" fixed modified. I'm glad my 1100's, 870's and 11-87's are a bit older. I'm a Remington field gun diehard but as of the last handfull of years (5,10,15 yrs.)they have gone down hill in quality and selection. But, this is just my opinion.
The newer 1100 G3 is just a glorified field gun with a big price tag and I feel my late 70's and early 80's 1100's are better guns. Only my opinion.
But I'm sure you are trying to get opinions on target guns. This is where I'm fortunate enough to own Beretta target autos. My only Remington purchase that I've ever been disapointed with over a 30+ year period was a recent (few years ago) new Sporting 12 1100. Has a real lot to be desired quality wise and again nothing but a glorified field gun as the G3. As much as I tried to get use to this gun I could never make it happen. It cycles perfectly but the barrel just never wants to stay tight into the receiver. It slightly works itself loose. Between stations I have to take up on the barrel nut. I find this to be a major distraction during shooting. The old style barrel nuts will never work loose and have a better design. I got so annoyed with this issue I turned to a Beretta auto and never looked back. The gun has become a loaner gun to new and first time shooters I take out. If you are looking for a field gun the 1100 and 11-87 can't be beat. The quality, fit and feel of the Beretta target autos are far superior to the Remmys. This is just my opinion. Good luck.
You can epoxy the feed latch in place. I did this about 5 years ago with my 1100 and it has worked flawlessly ever since. Clean the receiver and feed latch well with alcohol, mix and apply 5 minute epoxy in the groove, insert feed latch and clamp in place with C clamps. From then on, always remove and install the trigger pins TOWARD the ejection window. This will keep the feed latch from being knocked loose again.