I'm a bit (a lot) biased but think I can toss in some extra details not already covered in the comments.

tl;dr - CSN:Z offers a ton of content 'out of the box', CS1.6 potentially offers infinitely more but it must be found or hosted. If you only want DE\CS maps and nothing else, CS1.6 may win out. If you spend more time playing server mods, such as zombie modes, CSN:Z may win you over.

•CSN:Z gets regular updates of content and events. CS1.6 relies on community made content and independent servers to host said content. Not inherently pro or con in either case, rather different strengths for different play styles and priorities. (steady influx of Nexon-made content but only that content VS irregular making\finding player made content but far more content)

•CSN:Z is a consistent and persistent experience. There's lots of server mods and maps that I really love from CS1.6 that are not available in CSN:Z, but at the same time I have little control over how long I can enjoy such content if I find it in CS1.6 Say I find a CS1.6 server running 24/7 FY_Pool_Day, hooray! A month later this server might be 24/7 Dust2, or just removed entirely, Boo. Nothing I can really do about this if it happens and will need to re-find another server hosting what I want. My route to prevent this is paying cost&time to host my own server and never change what it offers.

•New guns and weapons, but options to disable guns\weapons as well. All the CS Classic stuff is available permanently without any cash or points-shop steps, but there's also a damn lot of new guns developed by Nexon. Hooray for lots of new guns, but that could just frustrate players who prioritize the balance of AK\M4\AWP\Deagle. Options are in the game to make games which either prohibit the zombie-mode-focused weapons or just restrict to only CS Classic weapons.

•CSN:Z is free to play... while that might be a 'duh' bullet point, it's worth listing in the context of convincing friends to form a group and play together. CS1.6 is not a huge sum of money to pick up, but that is still a hurdle towards convincing a friend to give it a try. A pro of CSN:Z is the ease of getting others to tag along with you, and both PvP and PvE modes can be a lot more fun with some buddies.