OK where to start.
Boot Camp: Not much small arms training here, basic marksmanship stuff. There just isn't the facilities in Great Lakes.
Fleet Training: Basically, the fleet small arms instructors go for basic weapons training. How to load, field strip the weapon, and qualify on a course of fire to demonstrate competance with the weapon. The purpose here is to get people qualified to stand watches. There is a push to get firearms simulators, PRISM, FATS, Beamhit systems, etc., to the fleet. Also the requirement for qualifications has increased, meaning we have to shoot more. This is where training can get really good if you have some creative Gunner's Mates and a CO who doesn't mind shooting alot.
Schools: This is where the Navy is doing better. There are currently two shooting schools and one tactics school meant for the average sailor. One shooting school focuses on refining marksmanship. The other school is a stressor course. The tactics school is probably the most practical in that it's force on force using Simunitions or paintballs depending on the facilities.
The last two years has seen the Navy moving in what I think is the right direction. The argument will always be that we can do more, but the whole picture must be taken into account. The Navy, by and large, employs systems when going to war. We don't employ many individuals to engage in actual combat. Of course those individuals that do get much, much more small arms training.
As it stands now most fleet personnel get just as much or more firearms training than most police officers in the country.