I have amano shrimps in one tank, cherry shrimps in another and nerite snails in both. The nerites are the bigger red and tiger ones rather than the smaller horned ones. I also have a small black and yellow striped snail (similar to horned nerites) in my betta's tank.
The larger snails do make quite a bit of mess, but they also seem to like rasping at the wood in their tanks and the mess looks like wood that's been through a snail's digestive system - the mess is usually underneath the wood. My betta's tank doesn't have any wood, and the small snail in there doesn't make nearly so much mess.
Cherry shrimps can also make a mess. Mine were in a tank on their own to grow out some juveniles before they went in a tank with fish and there was a lot of mess in that tank, but sort of finer than snail poo. I can't say exactly how much the amanos contribute to their tank, but it is quite common to see one with a string of poo hanging from it.
I should add that I have sand in all my tanks so the snail, shrimp and fish poo is very visible. But I'd still rather have nerite snails than not.