Re: 308 but a .344NK?
Closer the chamber dimension is in neck means you work the brass less. Lets say you are running Win brass which has a loaded neck diameter of .336 and you fire it in chamber with .344 neck, you move brass 0.004"/side. If you have a .342 neck brass only moves 0.003"/side.
F-class rifle I like to have minimum of 0.0015"/side clearance between loaded round neck diameter and chamber diameter for neck.
Tactical rifle, I like at least 0.002" for the largest loaded neck diameter for any ammo that might be used. Lets say running LC brass, about 0.340" for a loaded round neck diameter so I'd run a 0.344" to give me 0.002" clearance a side.
Main advantage to a "tight" neck is that you can limit how much you work the brass on each firing. Reduces need to anneal case necks to remove the work hardening. Disadvantage is you limit yourself to a single brand of brass or have to neck turn cases to maintain clearance.