I've never traveled in F {little point as I don't drink Champagne}, but from what I understand from reading many threads on similar subjects over the years, I've generally see F has being more Private - more personal space, etc. than you will get in C - when travelling on the same airline

In C you may have extra comforts that let you work or arrive refreshed enough to go straight to work (e.g. Lie-flat seats, decent meals, Lounge access, on board laptop power/internet), but you don't necessarily get the personal space. You are likely to have to still sit next to someone you don't know, and may even have to climb over them (or v.v.) on some airlines*.

With F service, you get some space, both in the lounges and in the air.
And the crew are more likely to avoid disturbing you - e.g. if you want to eat halfway through the flight, they'll likely accommodate it, whereas in C it's usually either a 'No can do', or the times available being limited.

Quality of products in F should also be a bit higher too.

* {if you want to access the aisle}.

The key point to remember is C and F on the same airline.
Taking F on one airline and comparing to C on another is similar to comparing Apples and Pears - not a fair comparison.
An airline with a crap C offering is likely to offer a somewhat less crap F offering, but a decent airline offering great a C experience will likely offer a superb F package.