I got a Mystery Snail for Fishie once, and he attacked it twice within the first 20 minutes it was in his tank, including biting off one of the eye stalks, so I had to move the snail to its own tank (and then it died a week or so later... I'm not sure that it was from the betta attack, though).
Now I have a 10 gallon divided tank for my 3 bettas and I have an algae problem, so I decided to get 2 nerite snails. I didn't put one in Fishie's side because of the way he acted with the mystery snail, and I was wary about putting one with Jasper because of the fact that she bites my finger whenever I put it in the tank. But there hasn't been a problem. She got really curious at first and would swim up really close and stare at him, and one time she pecked him when he was on the glass (not hard enough to knock him off, though). Now she pretty much ignores him.
So I think you should probably remove the snail if he's always being harassed, but maybe try to put him with your other betta, even though he seems more aggressive- he might be like my Jasper who likes to chomp human fingers but doesn't have a problem at all with a snail.