Ronaldo hit a personal-best 61 goals last season in all competitions, but Real Madrid went trophyless under Carlo Ancelotti as Messi’s 58 contributed to a famous treble.
Alves, speaking on ESPN’s Brazilian football programme Bola de Vez, did not hold back as he compared Messi with the 30-year-old Portuguese international.
“Messi is much better than Cristiano Ronaldo,” he said. “Messi has an influence on the play and Cristiano doesn’t.
“See if he has an influence on the play beyond scoring goals and appearing in certain moves. Messi is influential, he plays and assists. Messi has a divine gift.”
Ronaldo was criticised last season for appearing not to celebrate goals scored by his team-mates, and Barcelona’s Brazilian right-back Alves has accused him of not caring for the team.
His 61 goals in 47 appearances included 19 assists, while Messi made 26 goals.
Alves added: “He has things that I do not admire because I play for the team. I think that my team is more important than me.
“I think he cares little for what really matters, which is the collective side of the game.
“So much so that some criticised us during the celebration of titles while he celebrated the Pichichi (top league goalscorer award).”