All of the features will be unlocked with the C701 since its only purpose for being built was to control the H701.
The Alpine H701 has a built in active crossover that can replace your passive crossovers going to your front door components (which consist of a tweeter and a midrange). The outputs on the Alpine are labeled Front 1, Front 2, Rear, and Subwoofer. This allows for the option of amping your tweeter seperately with seperate inputs. Front 1 could control your tweeters, Front 2 would then control your midranges, and the rear and subwoofer would be the same as before. It's just an option for added flexibility. If you would rather just use your passive crossovers that came with your components, than you can just use either Front 1 or Front 2 (but not both).
As for the European Version, I'm pretty sure that it is the same version because my owner's manual was written in three languages (French, Spanish, and English). That's not necessarily proof, but I wouldn't doubt they are the exact same product.