I had both, one HD600 bought in 2013 (batch from 2012 according to its marks on diaphragm), one HD650 bought from Thomann in March 2017(february batch), a pair of HD650 drivers bought from Audio Sancturay in January 2018 (batch from March 2017) and the most recent another pair of HD650 drivers bought from Audio Sancturay (again) this year (batch from March 2019, quite old, I have no ideia if this batch is already included in the new release). So, I spent 7 years with a HD600 and at least 2 years with 2 pair of HD650s.
I did some tests during all this time and I could tell all the HD650s apart (I did some measurements as well) from each other as well the HD600. About the HD650s, the one from Thomann had the shortest bass extension among this model but stills "higher" than the HD600 - although I have had two pair from close batchs, they sounded "differently" enough to tell apart. And more, besides the first pair from AS has more bass extension, it had a attenuation around 2kHz to 5kHz making it sounds a tad darker (see drive link bellow - it is possible to observe the bass extension differences as well). The last pair sounds the best for me, it is a mix from the two other, nice bass extension and no attenuation.
About the HD600 (I gave it last December few days before Christmas to my aunt - she's really happy BTW - so I have access to it): mid and above it sounds pretty similiar to the most recent HD650 but it barely has sub bass. It barely can reproduce the sub notes on Doin It Right from Daft Punk - that is the most notably difference.
Last year I was playing with some mods and one of them was to damp the back of the driver (I post about it here,
@solderdude gave me some tips BTW) to reduce the 100Hz hump on HD650 - it seems to has no influence on sub bass extension if did with care. Even doing it (reducing around 2~3dB) I could tell apart all the 3 HD650s (modded) from the HD600 even if I force it with EQ or modifying. It seems its driver can not hit hard enough (I don't like this term but) seeming "slow", bringing a muddy sub bass when EQ'd. It can be my unit...
About the tests, sometimes I asked someone (ex-girlfriend cof cof) to mix the HD650 (2017) drivers in pair replacing them without I'm seeing and I was able to tell which was which. Once she put one driver from each batch in the headband, I couldn't tell exatly but this "mix" sounded kind of blurry. I wasn't able to do this with HD600 because I could see the different driver texture.
(Measurement of the two HD650 with same pads - yellow: HD650 febr 2017; violet: HD650 march 2017)
https://drive.google.com/file/d/1N8OR5yHro2PvLva5zj1KCyx_0l_qOcdp/view
That's my two cents...