I'm partial to a couple of headphones in that range. I like the Focal Spirit Classic. Its quite neutral, beautiful mids and punches low in the bass. Its relaxing, never harsh. Such a beautiful sound it will make you literally freeze with it's amazing tone.
I'd pick them over the HD650/600. Amp wise they pair well with almost anything I've heard. Fiio E11, Vali are the ones I like to pair it with.
The HE400i
Great planar sound, up close mids, deep thick bass and detailed but not overly so treble. This is probably the best headphone in that price range. Amp wise E12 is fine as it's efficient.
HD650, best mids in it's class. Good bass and relaxing treble. I love this headphone!
Drove it with the Valo, good sound! E12 also.
HD600 vs X2
Two different sounds. Ones more balanced while the other is a bit U shaped. HD600 is more seductive sounding, creamy and relaxing. The X2 is a party animal headphone. It's bass goes quite low and the treble is detailed. Sadly the sound is hard to listen to with good vocal work. The soundstages are different, X1 is a bit airier as it's leaner. The 600 is quite good though considering it's lusher sound. Technically the 600 is a bit more articulate and refined sounding.
Depends on your prefer there! Sound is complex it's not as simple as A has better mids than B.
I vote Focal Classic, they are phenomenal, plus you can take them portably.
Good luck!