Neck thickness (not width) on a Jazz Professional V

[hyp.spec]

I'm in the market for a Jazz Professional V, but will have to order one blind and there's seemingly nowhere around here that have them.

I'm a big fan of the Precision Professional V and love the chunky neck. How much thinner is the Jazz neck?

The Precision has a '1963 C Profile' while the Jazz has a 'Modern C' profile.