I have seen this question askd many times and it is one most difficult to answer becvause it is always followed by that other question 'what are you looking for?' should we judge the ideals of european architecture with that of the middle east? Irish with italian? Chinese with Canadian? Gothic with Baroque?
i have been lucky to travel many places in my life, the USA extensively. Though i've tried, i have rarely warmed to American citys. Yet 4 continully spring to mind when i think of good architecture - New York San Francisco New Orleans and to a lesser extent Chicago. The first 3 regarding mostly earlier styles with the latter being generally for the contemporary.
However of European cities which i have always felt are more diverse and rich i would agree Paris Barcelona and for me perhaps Vienna.