To me, the biggest difference is bass and probably the soundstage if i understand the term correctly. HD650 feels very.. narrow? It's like the music is very close to ears (obviously not closed-cans close), but at the same time very distant if that makes sense? It's right HERE, but not really. Very strange sound. And it becomes even more apparent when i put on X2's. They sound really wide, i can't even tell where the sound is coming from, because it feels like sound originates somewhere outside the cups. The bass is superior, it had more punch where it needed. Also, X2's draws you into music, while HD650 produced music disappears. It's not engaging.
You shouldn't be using high gain on the X2 because they're very low impedance. Do you have the switch on the Magni 2 flipped for high gain (rear switch)? The 600 might need it, but the X2 definitely shouldn't use it.
If you are using high gain like Luckbad said, it is possible that you amp is in high impedance mode (not sure what the output impedance of the Magni 2 is in high gain). Note the X2 has a large impedance hump in the bass area but still south of 45 ohms. This can result in even more bass out of the X2.
As for the soundstage, maybe just double check that the HD-650's are wired properly...
Do i have to re-educate my ears?