The AKG K500/K501 and the Sennheiser HD580/HD600 do classical music very well. They both have relative strengths with regards to classical music. The AKG has a wider soundstage which can portray the sense of scale of a large orchestra better, a sweeter and more detailed midrange, and a brighter tonal balance which make them better at certain instruments than the Senns. However, the Senns have more warmth for instruments that benefit from it such as cello, a stronger low end with more extension, stronger dynamics, and slightly better reproduction of the timbre of many instruments in my opinion.
You decision will ultimately come down to what type of classical music you listen to and what sound signature you feel you would enjoy more. For example, if you listen to a lot of organ music the K501 is a no-go since it has neither the extension nor the power, but if you listen to a lot of voice recordings the K501 would likely be a better choice.
If you're willing to make the jump, you have another option in the form of electrostats. It might be a bit more difficult nowadays to get Stax on a budget of 300 euros since the prices have risen lately, but if you're patient you should be able to get some vintage Lambdas and a transformer box for about your budget. You'll need a speaker amp to power the Stax if you're using a transformer though; if you can somehow score a Lambda and an energizer for that budget, then you can just power the Stax from the energizer. I don't want to say too much about the sound since I just got my pair so I'm still on the honeymoon, but this girl can do classical. At the very least, my Stax are definitely faster and more detailed than either the K500 or the HD580 with an excellent tonal balance to boot.
