My impression as a Swede is that American traders and investors are more sophisticated on average. That's why I hang out here. Sophisticated might not necessarily mean profitable though, if you belong to the "day trade according to some indicators without an edge" crowd.
Even if it could be proven beyond a reasonable doubt that European traders were better than US traders (or vice versa) we'd be no further forward unless we understood why. There are a few differences I have noted amongst US traders that surprised me (as an English trader) - US traders hate to short the USD in forex US traders are less comfortable using percentages to define price differences, more comfortable using pips or points or dollars & cents US traders very readily rate stocks according to share price, rather than company characteristics like market cap etc.: the higher the price, the better the company!?!? There are also some structural differences between the US and British markets - UK traders can short anything as much as they want: there are no pattern day trader rules UK traders can spreadbet almost every major instrument: minimum stakes are pennies, minimum deposits are tiny UK regulation is really strict, at least compared to some European jurisdictions I've got to add I've had almost no contact with continental European traders, too little to generalise as above. On English language forums they're far more rare than Asian/Australasian traders.
The Cfd and spread betting providers in the UK and Europe have to put on their websites what percentage of customers are profitable. 74% of IG index clients lose money.