Verstappen earned his first win of the season at the previous race in Austria, which launched him to third in the drivers' championship, behind only Hamilton and the second Mercedes of Valtteri Bottas.
Horner said after Verstappen's Austrian win that he had "thought for a little while" that Verstappen is the best driver in F1, and at a media event ahead of this weekend's British Grand Prix was asked if that meant he was even better than Hamilton.
"As the form driver, he is," said Horner. "As the driver in the form of his life, arguably over the past 12 months, he's been the best driver in the world.
"How do I substantiate that? He's not in the best car. But when you look at the results he's got out of that car since Montreal last year, some of the performances he's put in, he's made virtually zero mistakes in that period.
"It's only natural that there's always the next generation coming. Lewis has got the benefit of experience, he's still extremely quick, he's in the best car, in a very well-oiled machine.
"Max is very much the coming man. Wouldn't it be fantastic for the sport to see those guys go head-to-head?"
Horner said he would "absolutely back Max" to come out on top in the same machinery as Hamilton, who has won four of his five world titles since joining Mercedes.
In a 24-race run that started at last year's Canadian Grand Prix, Verstappen has scored three victories, 10 further podiums and not finished a race lower than fifth.
Horner believes Verstappen has also "really changed" since Daniel Ricciardo's departure to Renault promoted Verstappen to leader alongside Pierre Gasly.
"Daniel is such a big character, with a big sense of humour," said Horner. "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 added that there is "no sense of entitlement" with Verstappen, who entered F1 as a 17-year-old and won on his Red Bull debut when he was hastily promoted to the senior team at the 2016 Spanish Grand Prix.
"He's passionate," Horner added. "If you go back to the issue with [Brazilian Grand Prix shoving partner Esteban] Ocon last year.
"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."