HD600 all the way. Haven't heard the Grados though but looking through reviews they seem to have a coloured and fun signature which in my experience don't suit classical music. The HD650 also had a coloured signature and the bass is too much for my taste, classical being my primary listening genre.
It still depends on your personal preference. I love bass when I listen to pop music. To me the HD600 makes the timpani slightly too boomy and is slightttly overwhelming in symphonies, but the lower strings sound great. I'm a violinist so I like the higher notes xD and the AKG q701 has just the right amount of bass for me. I also have the ATH ad500 but those are actually too bass light lol.
The HD600 actually has the right amount of bass imo. I play the violin as well as other instruments including the timpani (maybe I should become a conductor ).