It has been a loooong time I haeard 650s at friends's - and yes, s500 is way more realistic with classics. 600/650 never appealed to me after electrostatics, s500 does.
My current s500 setuo is AT velours, all 3 ports taped over, with some damping inside cups. They do miss low end extension of Stax Lambda Pro, they still tend towards shouting at certain high(er) frequencies and can be very annoying with some piano tracks - but they are quite outstanding in most other areas with classics. I find the stock pads way too bassy and closed in in the treble - not that I feel using any other pads is wrong, just saying what I found the best compromise for my ears so far.