The 43-year-old feels that the Portugal international is nearly flawless, and he tipped Los Blancos to go all the way in the Champions League this term
Both players are widely regarded as the two best footballers in the world at the moment, but the former Los Blancos forward has a clear preference for the Portugal international.
"They're very distinct players. Their way of playing and moving is different," Mijatovic was quoted as saying by Marca.
"But, for me, Cristiano is better than Messi. He's a more complete player. He's faster, more explosive, he uses both feet, is good with his head.
"For me, Cristiano doesn't have any faults. If I have to choose, I'll go for Cristiano."
Mijatovic also had his say on Madrid's Champions League chances and head coach Jose Mourinho, and believes the Portuguese is the right man to guide them to European glory.
"It's Mou's third season as coach and the team is mature enough to win the Champions League. Its time has come.
"Mourinho is the best coach in the world. I have no doubts about it. I'm optimistic because, although there's a long way to go, Madrid have a quality squad and almost made it to the final two years running."
Real Madrid are currently preparing for Wednesday's away game versus Ajax.