I have kept tanks with hermits and without, and really have not seen any differences in the tanks with or without them. It seems pretty clear that if they survive/thrive in your tank that they are indeed finding food, which means they are cleaning 'stuff' up that nothing else wants or can access. Whether that is truly important I can't say. Logically, if they are finding uneaten food and consuming it, then they are doing something to reduce nutrients in the water. Whether that's a measurable effect remains to be proven.
However, comparing hermits vs snails as members of the cleanup crew is both meaningless and irrelevant. They serve completely different purposes, and one simply cannot replace the other. Even detritus-focused snails cannot access many of the areas a hermit crab can. Likewise, a hermit crab will do little for the sand bed, and nothing for the glass.
I have occasionally seen hermits munching on algae, but they are just not large enough to impact a serious algae problem unless you have huge numbers of them.
Other than climbing onto them, I never saw crabs bother any corals or polyps at all.
I don't have any crabs in my tanks now, and am not rushing out to buy any anytime soon.