To add my ten penneth-worth ...
As most people have already said, the C64-C was the most common machine produced for the UK market, making the original shape (often referred to as a "Bull Nose"). I think it was after the release of the desktop version of the 128 (128D) so that it was uniform.
I think the keyboard is much nicer on the original - it is more tactile. Well, mine is anyway. I sold my C64-C (which funnily enough was exactly the same pack as the one on the link at the beginning of this thread!). I had no reason to keep it and got rid of it for about £20.
Rare? No. Collectible? Well, it depends on how much you like to collect Commodore kit.