A friend who changed from wet to dry saves 40 gallons a week of fuel now. Most seem to think it is because you are not wasting energy pushing that exhaust all the way to the stern. I have dry exhaust and a heat exchanger. There are plenty of new builds with dry exhaust out there too.
I've never heard of saving fuel going to dry exhaust, but I've never switched from one to the other on the same boat. As long as back pressure for either system is within manufacturer's spec, fuel burn should be the same.
On my dry exhaust systems, the bottom flange of the muffler is mounted at deck level, the muffler is wrapped with an exhaust blanket and the muffler is contained in an aluminum box/shroud that is vented on the sides and top of the shroud (see pic)