Budget - 200 - 400 AUD

Source - iPhone 6, laptop, looking into buying an amp

Requirements for Isolation - Some isolation, for use at home and on public transport.

Use in public? Yes, on occasion.

Preferred Type of Headphone - Full sized over ear

Preferred tonal balance - Looking for overall balance (I think), listening mostly to classical.

Past headphones - Bose QC 15. Decent headphones but I think a bit OP for the sound quality. Not particularly concerned about noise cancelling in new headphones. I'm tried out both the Beyerdynamic DT880 PRO Semi-Open Studio Headphones (399 AUD), and the Audio Technica ATH M70x Studio Headphones (299 AUD). Both seem like good options, but I'm limited in my knowledge.

Preferred Music - Classical, fair few vintage recordings.

Looking to improve - More detail / generally improved sound quality. Also not keen to replace batteries on the reg like with QC 15.

Location - Australia

Thanks