THIS IS GOING TO BE A HOT TOPIC.
The problem is that there are a lot of strong opinions. There is some cork-sniffers that will start bitching right away. BUT... maybe I am a cork-sniffer myself. Oh-well.
I am not going to get into the chemical makeup and application of either, you can Google that yourself.
There are a few pre-requisites on this though. First off, some are hand sprayed and some are done by machine. Some coats are thicker than others, some poly seem thicker, and some are really thick and i hate that. The 'stickiness' is irrelevant between the two, as you can go over the back of the neck with some #0000 steel wool to get it slipperier. *IF you do this make sure you have your pickups taped over so you don't get metal dust in there*
I own twenty-ish guitars at the moment and five are nitro (all Gibsons). What i love about nitro, is that feels much smoother and silkier on the back of the neck. Its a beautiful feeling to slide down the neck on a properly finished nitrocellulose neck.
My poly guitars, (at this point mostly Ibanez Prestiges and USA Fenders), feel great too. In my opinion the best feeling poly necks are done on the Ibanez Prestiges. They play well, and applied thin. USA and fenders are pretty good too, but some i will take the finish off of the back of the neck and apply a rubbed on finish, which I love too.
So over a decade ago, I had this Washburn X-50 PRO. It seemed as if the finish was so thick that the body was suffocated by poly. It was dead sounding. A few months later, I chipped it. I will be damned if the finish wasn't as thick as truck bed-liner. I ended up selling the guitar shortly after, thoroughly disgusted. That is one reason I don't buy cheap poly guitars.
Nitro DOES WEAR though, and it can be fast. I do not have my former #1 Gibson (not on me at the moment), but a lot of the finish is through, but it got beat for EIGHT years. The only reason I am not using that guitar is that it needs a re-fret (if I get lucky I may get by with a level and crown). Nitro also checks/cracks if exposed to the harsh elements, I have that on there too. BUT the neck is just yummy. sooo damn yummy. One thing about nitro is that it is more breathable and to me it feels more natural, and only feels better with time.
Some say nitro is thinner SO it sounds better, I call bullocks on that. Poly is more durable on the surface and doesn't scratch on the surface as easily. Nitro is easier to repair, which IS a good thing. I have never seen a nitro finish as thick as a thick poly finish.
In conclusion, send your hate-spam.