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Both ships offer a very good product and it's a rather close call. The major difference lies with the size of the two ships and the range of activities they offer. The "Regatta" is a smaller ship by today's standards which doesn't want to offer constant entertainment, making the product a more relaxed one. The "Millennium" on the other hand is a large ship with lots of organized activities.
One thing one has to take into account IMHO is that "Millennium" has been plagued with propulsion problems recently. The four "Millennium"-class vessels feature a so-called podded propulsion system which tends to cause trouble fairly regularly. While this isn't a safety issue one must know that there is a somewhat higher chance for cruises on this class of ships to be cancelled for technical reasons than with other ships. We're talking about a very small percentage of all these ships' sailings, however, and personally I wouldn't mind booking them despite of that. Actually my parents will be disembarking the "Millennium" on the day you might be embarking in Barcelona.
Yet, if you ask for my personal, very subjective opinion, I would would prefer the "Regatta", simply for the more personal size, the excellent service and the second-to-none food. Of course there are others who wouldn't want to be onboard such a tiny [sic] ship.