Is there any advantage to having a thicker neck radius? What's the difference in feel between playing a larger radius (say 12") to a smaller one (say 9.5")?
It depends on the person, some like thick necks like me, or others like thinner necks so that they can move faster.
Lets jump in a pool

Last edited by I am wet : Today at 03:26 XM.
There isn't really any kind of advantage either way. It's all about what you're comfortable with and what fits in your hand. Thinner necks tend to be easier to play on to an extent but really it all depends on what you like the feel of.
Neck radius =/= to neck thickness. Radius has to do with the thickness/roundness of a fretboard.

For example Ibanezs have a very flat radius of about 15.5" whereas old Teles have a much rounder radius around 7.5" sometimes.
The flatter radius is easier to bend and "shred". The smaller radius is easier to play chords on but bends tend to fret out if you try to bend to high a note. Many many guitars come with 12" radius. It was old fenders that came with the 7.5 and 9" radius. Some of the new ones do and some have flatter radius. My fender is 12" as is my LP. Or if you want both you can get a progressive radius where it starts at 9" at the nut and flattens to around 16 at the heel.