The Atletico Madrid president believes that the Frenchman is more tried and tested at the top level than the Colombian, who moved to Real Madrid this summer
The Colombian completed a move to Santiago Bernabeu from Monaco after starring for his country at the World Cup this summer, where he won the Golden Boot as he inspired them to the quarter-finals.
However, Cerezo feels that Griezmann, signed from Real Sociedad for around €25m, is more used to top-level football in Europe and believes he could be as influential for the club as new Barcelona signing Luis Suarez.
"Antione is a player who is more tested across Europe and is the signing of the summer," he said at the Frenchman's unveiling.
"[Griezmann] is comparable to players like Luis Suarez. He's a great reinforcement for the club and we made a great effort to bring him in.
"Though I had many offers, he decided on a serious and important club like Atletico.
"We don't know about James because he still doesn't have a defined path."