I'll keep things short and sweet.

What's the difference between the necks of these two guitars?

I'm not very experienced, so numbers won't mean too much for me.

Which one fills the hand more, and how do they differ aesthetically?

I think the Classic series neck had a darker tint...does CP 60 have that tint as well?

The CP 60s has Medium jumbo frets vs the Classics vintage ( small frets),
and the CP 60s neck is a 12inch ( Flatter radius) and the Classic is the vintage 7.25" ( Rounder). Also in my experience the Classic Player neck is slightly beefier, flatter so it doesn't " Fret out" on bends. The Classic neck is rounder and so supposedly it feels better for chording., while the CP is more comfortable for lead work. I have owned a CP before and it has a pretty nice neck. Also both are tinted and gloss

Thank you so much for your answer!

I currently have a Clapton signature, which apparently has a 9.5 radius. Which out of the two 60's guitars would be closer to the Clapton? (i know 9.5 is pretty much in the middle numberwise...sorry for asking this )

The clapton also has a soft V shaped neck, while both of the 60s have C shapes, so neither will feel much like the clapton, but the Clapton and the CP both are flatter than the Classic, and they have the same fret size IIRC.

I had the chance to try out the Classic 60's neck, and it actually felt really nice.

It filled (?) my hand better than the Clapton neck, and I WAS interested in buying a C neck so I could try out different types of necks.

I really liked the neck on Classic 60's...Only wish I could have tried the CP 60's which the store didn't have...

Do they have the same neck profile, ie. fill my hand the same way?