Working Cockers usually have less coat, so although I expect they moult in the same way there simply won't be as much hair flying around.
I don't see why either type should be more or less affected by teeth or gum problems. I believe there's probably a genetic element in dental problems, much the same as in people, where some will naturally have stronger teeth and healthier gums. Diet can also be a factor, but I've never heard it said, or seen any evidence, that working Cockers are less likely to be affected.
I'm not sure about ingrowing eyelashes. I've always had show types and none of them has had the problem, but I know that as a breed some Cockers are affected by it. I don't know if it's a genetic issue.