We should just agree upon that this is your personal and subjective point of view described with words that you find suitable. Not a definitive description of how these headphones actually sound. (It is still possible something is wrong with your pair)
Many people on this board feel quite the opposite. If great tonality and timbre, naturalness, neutralness and flat frequency response are not high fidelity then I don't know what is. We could also conclude that the way HD650 colors the sound is quite opposite to high fidelity.
I have them both. Both are nice headphones but with HD600 you get beautiful and euphoric sound, great tonality and neutralness, nice imaging and airiness all in one package. HD650 just sounds bloated in the lower regions and colored and, imho, a step further from the true high fidelity compared to HD600.
HD650 are still very enjoyable headphones if you want to relax (and fall asleep
to your music) Just my 2 cents