The debate about who is better is one of football's hot topics, especially as the pair are believed to rival each other for the Ballon d'Or title.
Messi and Ronaldo scored 148 goals in all competitions for club and country last season, but Alves believes that the Argentinian has the edge over his Portuguese counterpart.
"What puts Ronaldo below Messi is not behaviour," Football Espana quotes Alves as saying. "It's Messi's ability to play football.
"Leo has a gift and it's not a thing you can work on. That is what sets them apart."
The winner of the Ballon d'or will be announced in Zurich on January 7, 2013.