Hamilton currently leads the championship and Verstappen is in second, with the duo coming P1 and P2 in the last four races - Hamilton winning three and his Dutch counterpart winning the 70th Anniversary Grand Prix.
Verstappen is consistently challenging the two Mercedes despite having a significantly lesser car on paper and were it not for his DNF in Austria, where his car had a mechanical failure when running in second (in front of Hamilton), the 22-year-old could have been right behind Hamilton in the standings.
After another impressive drive at the Circuit de Catalunya, Horner praised his top driver for squeezing the maximum out of the RB16 yet again.
"I think that was the absolute maximum we could achieve today," he told Sky Sports F1.
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"Max has got everything he can out the car. To split the Mercedes who had a quicker car than us today, I don’t think we could’ve got more than that."
While it is always difficult to compare two drivers in different cars, Horner does not there is much to split Verstappen and Hamilton as pure drivers.
"They are the two in-form drivers in Formula 1, I think there is very little to choose between them," the Briton added.
"It’s interesting, you’ve got Max who's 22 years of age, Lewis who's 36 I guess or something like that . They’re in different stages of their career.
"I’m hopeful in the coming races that we see the two of them go head-to-head because I think that’s what the viewers would love to see, it’s what the teams would love to see, I think it would be good for Formula 1."
On the other side of the Red Bull garage, Alexander Albon had a much more difficult race, finishing in eighth.
The Thai driver tried a one-stop strategy but had to come in a second time as he could not manage the tyres, as he was in constant traffic and dirty air.
Albon eventually was lapped by Verstappen in what was a tough day at the office for the 24-year-old.
"I mean, we tried it," he told Sky Sports F1 when talking about pitting for the hard tyre.
"But to be honest, we had to pit around that time because there were no tyres left. I didn’t have any tyres on each stint.
"I don’t know what it is but it’s the opposite of Silverstone where… yeah. It was a little bit like qualifying but just… more. Just really struggling to keep the tyres alive."
Horner added Albon mainly "didn't have a good balance in the car", although he did move up a place in the standings, as he now sits sixth.
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