I have both a dedicated wet and dry vac. Both Shop Vacs.

The dry has a foam filter and 10-13 gal. paper filter. It doesn't get used more than 5 min. a week anymore.

The wet, with just the foam filter. Gets used for everything, extracting, vacuum etc.
The key is a wet foam filter. Water in tank would help to empty debris and keep filter wet.

I use a deodorent to keep the smell down, dog hair etc.

Personally i think the wet method is superior in a couple ways. It can be used as an extractor and vac in one go.

The vac seems to last longer, i always seemed to get a little hole in the dry paper filter and was blowing dust around and the vac would expired sooner, than my wet vac.