Dave, the two model you mentioned in your post are two different types of headphone, the AKG K240 Mark II is a HI-FI headphone. The Sony MDR-V600 is a studio monitor headphone.
I don't know anything about the Sony, but it is interesting about the AKG. Coincidentally, I just discovered the same thing last night. The AKG 240 used
to be a studio monitor headphone, but it apparently isn't quite that accurate anymore.http://wiki.faust3d.com/wiki/index.php?title=AKG_K240_Series
I have the AKG K240DF which is probably the best studio monitor version they ever made.
I think any headphones you like the sound of, "hi-fi" or otherwise, are fine if you're just using them for your own pleasure. But if you're using headphones to record with, or to evaluate the sounds coming out of an instrument, then you want to aim for something neutral, something accurate.
In terms of a moderately priced accurate headphone, I think the AKG of choice these days is the K702, though a Beyer DT-880 might still be a better choice, I'm not sure. Or if you want a closed back design, the Denon AH-D2000, which I just ordered, to complement my K240DF. It looks like they are almost as neutral, and will be handy when I need more volume, or am doing something in a noisy environment where I want to block out other sounds, or for microphone recording where the leakage of an open-back would be a problem.