Hmmm... as I've read through these great responses, it dawns on me that I may have made a mistake in my initial post:
the CZ 550 Varmint that I used as one comparator in the OP may have a heavy walled barrel, but is probably not an actual match barrel.
Am I right?
Is the CZ 550 Varmint no different in construction to a 550 American or Lux or any other model, other than a having a fatter barrel?
I started this as a theoretical question, but there is a practical reason for my question. It all this boils down to trying to make a choice. A choice based on understanding.
My existing .308 is heavily used (muzzle bore gauge read at possibly just under 7.63mm) and I want to replace it with a new one now as I will soon no longer be able to buy anything new due to up and coming commitments...
I like the shorter 20" CZ American, but I also like th beefy 25" CZ 550 Varmint. But the Varmint is almost €200 more.
Is that worth getting match barrel performance? Yes.
Is it worth just the look of a match barrel? Not so sure.
Based on the responses, it seems that a heavy barrel may not really offer me many more accurate shots than the standard if the barrel was not set against a square action face.
And so it follows that the only advantages other than the look of the Varmint, would be greater weight for stability and recoil. The extra 5 inches of barrel amy afford me some extra fps and hence range, but how much more and will I ever reach a stage where I can shoot that far?!
I don't anticipate needing any kind of rapid fire and don't yet have the necessary skill set, but nor do I want the option arbitrarily unavailable to me right from the get-go...
So final question taking range, accuracy, resilience to warming barrels, recoil and anything I've overlooked:
Realistically, in the hands of your average shooter (I'm no Zaitzev nor Bob Lee Swagger 
) what can the 25" Varmint do that the 20" American cannot?