Is this to be used unamped from something like an iPod?
Have not heard the Sony, but from what I have read they are too bassy and colored to mesh well with classical music. I have only briefly heard the Mag Dogs, so can offer no helpful opinion about them.
No amp knocks out some excellent options, like the Shure SRH 940.
That lead us to mostly portable cans like the Senn Amperior (or little brother the HD25-1 II) and Audio Technica ATHESW9A Portable Wooden Headphones.
If you can still find it, the Sony MDR-V900HD is also a good choice and should be quite a bit below budget.
I own the SRH940 and although they benefit from an amp, they sounds just fine straight out of an iPhone 4S. A free EQ app from Golden Ears, Accudio can really really help if unamped. It applies a special EQ based on Golden Ear's measurements to make the SRH940 sound neutral (it's special EQ has a 5/5 rating meaning the sound output is very clean-sounding I believe).