For all practical purposes on the trap line, there is no difference.
Some say the 1100 has slightly softer recoil. I'm of the opinion the 1187 has slightly softer recoil. It's so close it's really a moot point.
The main difference is that the 1187 has a gas compensation system that allows everything from light 2-3/4" shells to heavy 3" loads like buckshot and slugs to be fired from the same barrel. For the 1100 you'd need two different barrels.
And from a trap standpoint, that's also a moot point, because the 1187 trap barrel is a non-compensated 2-3/4" only barrel.
There are minor parts differences. Extractors are wider on 1187s and late model 1100s. The late model 1100s share the 1187 forend and barrel retention system. The 1100 uses a carbon steel magazine tube, the 1187 has a stainless steel mag tube.
If the 1187 you're being offered is a genuine Premier Trap, that means it should have a 30" trap barrel. These barrel have a step rib. It's slightly higher than the standard ribs. There is a slight step on it towards the rear where the slope and the top meet. The important part of this barrel is that it is factory backbored. A normal bored is about .727". This barrel increases to approximately .745", then steps back down just before the choke tubes. Because of this, a special set of choke tubes were issued with this gun, taking into account the pre-existing .018" step down in the barrel. These choke tubes are marked TRAP FULL, TRAP EXTRA FULL and TRAP SUPER FULL. The purpose of this barrel is to give better patterns. I have this barrel and it does as claimed. With cheap soft shot it gave better patterns than a regular barrel, because it distorted the shot less in the choke tube. It has a slightly better pattern with premium shot, because that shot is harder and resists distorting more.
If this 1187 is indeed marked PREMIER TRAP and the barrel meets the above description and it has the three choke tubes per above, and the price is right, get it.