I just went to a store the other day and compared the two headphones. The 650's and the x1's using my O2.
At the time of A/B ing I was using a MOON 300D as a dac.
This is exactly what my notes say with my comments between brackets: (Remember, this is how I percieve the sound! It's always safe to compare them yourself if possible)
X1 O2+moon 300d= Less detailed then 650. Deeper bass, better quality "more layers though the higher volume of the bass may make it easier to hear the layers", less punch. Soundstage is nicer, more distant. Still has a closed feel to it. "would probably be because of the deep bass, maybe I don't like deep bass?"
650 moon 300d + O2= Sounds closer. Everything has more the same distance then X1. Has a nice high SSS to the sound "No sibilance or S but higher like 10kHz" Sounds much the same as the X1 with less lows and a more sparkly high.
To say it in a better way, the 650 is the winner for me unless I need the bass. For electronic music like house I'd prefer the x1. The soundstage of the X1 is further away but the vocals are too close, the rest of the music seems harder to focus on with the x1. The hd 650 placed everything you hear on the same nice distance. It's a little bit closer then the x1. The 650 is also surprisingly more detailed then the x1. Do note that I used a pretty high end dac in my comparison!
But here's another thing. I bought the fidelio x1 for 190 euros. The store where I listened to the 650 sells them for 400 euros! That's 210 euro's more. While I find the 650's better, it's only a bit better and diminishing results kicks in here. For twice the price you get +20% performance. (with a high end dac, maybe with the t1 a little less) Since you're from USA (right?) you might not be able to get the x1 at a good price and the 650's are probably much cheaper on the internet. I'd go for the 650's if the difference is not that big.
If you have any questions ask them now while my memory is still fresh.