If made around the same time and similar pad wear/clamp reduction they should basically be identical. Maybe some tolerance differences but not sure if it will have much if any impact on the sound. New HD 650’s and new 6XX’s should have the refreshed pads so eliminates the sonic changes the pad refresh did. If one is older than a couple years it will likely have the old style pads and will sound a little different.
If you get a used one you may want to get new pads sometime down the road depending on the amount of wear they have and if they don’t sound like you hope. Some people like how they sound with worn pads more than fresh pads. And some may prefer the sound of the old pads. These headphones sound can be affected a lot by pad wear is why I’m mentioning it.
When the pads are taken off the headphone new pads will have a clear plastic ring on the rear whereas it’s matte black plastic on the old pads. I am curious about the pad wear difference between new and old pads as I think I recall one change was the new pads foam was supposed to keep their shape better than the old style which likely increases their lifespan and is likely less affected sonically by wear if true. *So far it seems true as my current pairs are retaining their pad shape and firmness better than I recall my pairs with old pads did.
Physically the HD 650 feels more premium in the hand than the HD 6XX, 600 (new ones feels less premium than the old granite finished ones), HD 660S/S2. This is due to the painted mold, what feels like a thicker grill, and the glossy plastic used on the earcups (matte plastic on other HD 6xx headphones).