The Amadeus Quartet was founded in 1947 by three Jewish musicians driven out of Vienna by Hitler's Anschluss in 1938. They all studied with violin teacher Max Rostal who taught them free of charge. At the time he was teaching at the Guildhall School of Music in London. Through him they met the fourth member, cellist Martin Lovett. A year after getting together they debuted at Wigmore Hall. Active from 1947 to 1987, they were one of the most famous quartets of the 20th century. Benjamin Britten wrote his Third String Quartet expressly for them.
As I mentioned, I can't find this performance on YouTube, but the Beethoven String Quartets performed by Amadeus are available on Amazon here:
You can go to the Amazon page and listen to a brief sample of the movement. It is the last track on disc 6. You can even purchase the track for $0.99.
As three-quarters of the group were Austrian and their teacher was also Austrian-born, you would expect their approach to be rather Viennese. I'm not sure how to describe the Viennese sound, but the violinist I have worked with the most, Paul Kling, though Czech, studied in Vienna and my impressions are that this implies a certain lyricism, grace and warmth of sound. I hear some of this in the Amadeus performance. I notice that the first violin does a glissando in that augmented second of the theme that appears in mm 22 and following. The performance has drive and gusto. It doesn't bother me in the least that it is a monophonic recording. The tempo is what I would call a restrained Allegro, not a "throw all caution to the winds" Allegro. But there is real passion without loss of control. Nothing at all wrong with this performance.