> The credit score system already in place in the US [...] Does Europe do it much differently?

Yes, as far as I'm aware the US & Canada are unique in having 'a credit score' for people; elsewhere there may be agencies offering scoring services to lenders, but it's not something individuals ordinarily nor need to care about, and it's not 'their score' it's just that particular company's (Equifax's, or whoever) rating.

It's not taken as seriously, nor does it need to be.