I've used both, been using canned Fluid Film NAS for at least 10 years. Started using Woolwax in a sprayer along with Fluid Film NAS in a sprayer several months ago.
The NAS (Fluid Film AS in a can, the documentation for this stuff has been terrible until very recently) is thinner and I think works best for hem seals and in enclosed spaces. The thinner extension tube for NAS threads into existing weep holes; I don't believe in destroying good metal to drill a hole to apply rust preventative to try to keep the metal... sort of doesn't make any sense. But you can't insert the fat sprayer tube in doors easily without drilling a hole, so I don't use the fat tube and sprayer and stay with NAS cans. Because I prefer the thinner NAS for hem seals, I don't use Woolwax for that purpose. For a brand new vehicle, I may consider Woolwax for a different reason-- the hem seals are clean and the creep is less. This is somewhat important, because the material will creep up the outside of the door, and accumulate dirt. My vehicles are old and I don't care that there is a gray/brown band at the bottom of the door and tailgate, but some people have time to burn keeping their vehicles waxed and shiny and may object to the greater NAS creep.
For underbody, especially areas washed by splashing from wheels and such, Woolwax is more effective than NAS. Much more effective. I use the Fluid Film grease for steel wheel wells, NAS washes off quickly, Woolwax more slowly, the Fluid Film grease holds up fairly well. With Kellsport going to Woolwax, getting the Fluid Film grease may be difficult as Kellsport doesn't seem to carry it anymore.
On experimental areas of surface corrosion where paint is peeling away and exposed to UV, Woolwax seems to last significantly longer than NAS although for critical areas I use Dow111 silicone grease which seems to last forever unless physically rubbed off (no UV effect, rain will beat it off after a longish while). I'd like to try Fluid Film AR or Fluid Film GEL BEW... but just try to get any of this material at some reasonable price.
Tools: the Kellsport more expensive sprayer works well, sprays very well with a smallish compressor. The sprayer works with AS and Woolwax equally well. The extension tubes are recommended-- ability to use the extension tubes is the reason for buying the more expensive sprayer, even though the lateral sprayer tube barely works and is disappointing (means much more slowly withdrawing the tube when spraying to get enough coverage). Getting into box frames and under bed tubes is essentially a no-go with the cheaper spray head, one really needs those extensions. The pour can lid is a waste of money unless one wants to use the pump gadget, the pump gadget pushes material out pretty fast. But the Kellsport lid doesn't stay on the gallon can so can't be used for pouring-- I use the Home Depot silicone gallon can pouring spout, cheaper and actually stays on a gallon can (I found pouring is much easier than using the pump thing to transfer to the quart sprayer bottles anyway).
What I would like to see is Kellsport carry the Fluid Film exotica, like Fluid Film AR (very thick) and hard to get items like GEL BEW. Sales may not justify the effort, it just appears that Woolwax doesn't have a comparable product line. For AS gallons and NAS there is Amazon; I still prefer NAS for hem seals and enclosed small areas. Jury is out for Woolwax cans for spot touch ups as the Woolwax in cans hasn't been out very long from Kellsport.
Finally, I like the smell of Fluid Film. Woolwax is nearly odorless, but the odor to me is like Desitin, and that isn't a compliment. The good news is that the material doesn't stink of carcinogenic hydrocarbons.