I'm European and I was circumcised roughly 9 months ago. I did it to cure Lichen Sclerosus (also called BXO) and had to go low to remove as much as possible of the affected inner foreskin. I also decided to go on the tight side for cosmetic reasons. I suppose this is neither American-type (low, not high), nor European (tight, not loose).
I personally wouldn't generalize about European circumcision, as the procedure, though far from extinct, is reasonably rare over here (10-15% in the UK I believe) and performed mainly by cultures who normally circumcise, and less so for medical reasons. For the former case there is quite a lot of variation, while the medical cuts tend to be on the lower side as they are usually performed to cure problems which involve the inner foreskin, which has to be removed. As far as I am aware, the only condition for which the NHS recommends circumcision as a standard treatment is LS/BXO, which can only spread to mucosal tissue, so the cut naturally has to be as low as reasonably possible in order to remove the affected skin and potential areas that could be affected in the future. Other than that, I'd say that circumcision is fairly rare outside of these two groups, so there really is not such a thing as an Euro cut as there is the characteristic high and tight done in the US.
In terms of functionality and effects of the two types, I cannot comment on the differences between them, but I can say that the alleged loss in functionality and pleasure for the low and tight cut is massively exaggerated from my particular experience (and I developed LS after starting my sex life, so I experienced normal uncut sex as well). I firmly agree though that circumcisions should only be performed for medical reasons or/and with adult consent. If that is the case, then the circumcision rate should be massively lower than it is, and for the ones which have to performed, low cuts should be the predominant style. The only acceptable reason for a high circumcision is aesthetics and it should be performed to consenting adults only.