I have an early Nitefly 2 (hss pickup config) which was my main guitar until I got a Fly Classic last year.
The neck is thick but I never had any problems with it. The early Niteflys (versions 1 and 2) had maple bodies. They were probably the heaviest guitars Parker had ever made. That said, its weight is probably average when compared to other manufacturers. They have a SS frets, a similar (not exactly the same) Parker bridge design with piezo, locking tuners, carbon/glass composite exoskeleton on the neck and similar outline to the Fly guitars, but thats where the similarities end. Later versions have different bodies, I think mahogany with 2 humbuckers and swamp ash with hss pickup config are the most common versions. I got my Nitefly for $750 new in 1998. I like them a lot but I wouldn't pay more than $600 for a used Nitefly. Mine sounded like a fat strat, but it with less ice pick highs and more bass. The tone was close enough that I never felt the need to have a Strat too (I sold my Hwy 1).
The Fly is very different. The bodies are much more contoured. Both the body and neck are thinner than a Nitefly and they weigh less than 6 lbs, some as low as 4.5 lbs. They have set necks rather than bold ons like the Niteflys. The exoskeleton not only covers the neck but also the entire back of the guitar. It is baked onto the guitar in a vacuum sealed oven. I got my Fly for $1300 used and I feel it was easily worth it. The tone is different, mine does not replicate a Les Paul or Strat, they have their own sound. I have tried Andersons, Ibanez, Ernie Ball MM, Gibsons, Fenders, PRS, and I have yet to find a guitar I like better. I do admit I'm kind of weird though, YMMV.
Niteflys do have one advantage over the Fly. The bodies are more of a normal depth so you can replace them. On a Fly, your options are limitied because the bodies are so thin. This was never a problem for me, I like the stock pickups on both my Parkers.