Sergei Nakariakov.J.Haydn-Trumpet Concerto in Es-dur.1Pt. - YouTube
Sergei misses the high Eb!(who wouldn't) He's playing the Haydn first movement on a Bb when he was in his early to mid teens.
A couple of years after I started to play trumpet, I printed off a copy of the Haydn sheet music. In my naievity I thought I could have a go at it. until my tutor at the time pointed out to me that I had the wrong sheet music and showed me a copy written for Bb trumpet.
My guess would be that anyone playing the Haydn in a masterclass for a top soloist would be advised to play it on a Eb trumpet, as all the top soloists pay the pieces on Eb. My train of thought bing that once your used to playing a Eb, its the best tool for the job.