Ricciardo left for Renault at the end of last season, leading to Verstappen being promoted to lead driver and Pierre Gasly joining from Toro Rosso.
Horner feels that Verstappen has taken on the responsibility of being the senior driver after being in Ricciardo’s humorous shadow when they were teammates.
Horner said (quoted by Motorsport): "Daniel is such a big character, with a big sense of humour.
"And Max always outside of the car came a little bit within Daniel's shadow and was the jokey younger brother.
"Since Daniel has left Max has assumed the role of the senior driver within in the team and the responsibility that goes with that.
“There's a different level of maturity, of direction and sense of purpose with him.
"That has really rounded the package with him."
Horner also praised Verstappen for being passionate and saying it how it is within the sport, part of the reason many fans follow him.
"He's passionate, If you go back to the issue with [Brazilian Grand Prix shoving partner Esteban] Ocon last year,” Horner added.
"That's part of the reason people warm to him. He's not afraid to say as it is. Is that a bad thing? I'd rather have a driver like that, that has that passion and fire in his belly.
“The sport is crying out for more drivers like Max Verstappen."