The 21-year-old Dutchman won two races last year, with a third victory snatched from his grasp after a collision while leading in Brazil, and ended the season fourth overall.
Hamilton, now 34, won 11 races for Mercedes on his way to the title while four times world champion Vettel, 31, was runner-up having won five.
"Max, if you look at his performance in the second half of the (last) year, was the second highest points scorer to Lewis," Horner told reporters.
"I don't think he lacks anything that they have, if we can provide him the tools to do the job. I think he's probably the driver that they fear the most."
Verstappen was the sport's youngest driver when he made his debut with Red Bull-owned Toro Rosso as a 17-year-old and the youngest ever winner at 18 at the 2016 Spanish Grand Prix.
Horner said the years would eventually take their toll on Hamilton and Vettel and saw Verstappen, now the main man at the team after Australian Daniel Ricciardo left for Renault, as heir apparent.
"I think his maturity has increased, we saw that during the course of last year. He’s just much more rounded through experience," said the Briton.
"He’s just more worldly, more experienced, he’s just in a better place to be able to deal with the pressures that are placed on him."
Verstappen hit the headlines after Brazil, when he was ordered to do two days of public service for shoving French driver Esteban Ocon after the collision.
He did one day by accompanying the stewards at a Formula E race in Morocco last month.
"He came back and went, ‘Crikey, these guys have got difficult decisions to make. Whether you penalise or not.’ I think that was actually a useful exercise for him to see the other side of the fence," said Horner.
HONDA PROGRESS
Red Bull have a new partnership with Honda this year after more than a decade with Renault, whose engines powered them to four successive driver and constructor title doubles between 2010-13.
Honda had a troubled time with McLaren before a separation and teaming up with Red Bull-owned Toro Rosso last year.
Horner said Honda had shown good progress over the European winter and morale was high.
"I think we’ve had a really collaborative approach and open approach with Honda," said the team boss. "Communication has been very honest and very open about areas of strength and weakness."
Red Bull's relations with Renault were fractured from the start of the V6 turbo hybrid era, when Mercedes began a period of domination that has now brought them five successive title doubles.
Horner was sure the Honda partnership would be very different.
"Effectively we’ve been paying for a first class ticket and you get an economy seat," he said of the last three seasons with Renault.
"An awful lot of frustration was born out of that... so I think with Honda, it being a true technical partnership, there’s much more collective responsibility from both sides rather than being a customer-supplier scenario."
Horner said Red Bull aimed to be more consistent across all circuits this year, rather than just those where engine power was less of a factor.
(Reporting by Alan Baldwin, editing by Ken Ferris)
Share
