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.
So, what are you planning to use one for?