The older type of neutron dosimeter is the Neutron Track Emulsion film badge. Like other film badges, it was very accurate, reliable, and a permanent record of exposure. I don't think these are being used anymore for personnel dosimetry. Once developed, it shows a number of tracks that can be counted to quantify the exposure.
The Lithium Fluoride TLD is a newer method, if you consider 1960's technology to be "new". It works much like other TLD's, and looks just like them, except for the shielding in the case.
There also is an albedo dosimeter - which means that it actually measures the radiation coming OUT of the body after being reflected. I don't know the exact combination of chips used in this TLD, but I remember that it has to be worn tight against the body to be accurate. Like most TLD's in use outside the navy, there are multiple different chips and attenuators corresponding to each.
There is also timekeeping - where you just measure the dose rate and multiply it by the time of exposure. Or, you can just figure out the ratio of neutron dose rate vs. gamma dose rate for the work area and assign a correction factor to the gamma dose to account for the neutrons.
"Primarily" is a broad term, that assumes that one method is used regularly. But, the people who work with radiation are the type of people who like to reinvent the wheel a lot - not because they are stupid, but because they think they understand the concept of roundness better than anyone else, and you can't talk them into accepting a common method when they can spend so much more time and money developing one of their own that is just about as good. So, if you can find two nuke facilities using the same dosimeter, they're certainly using them differently.
