Soundstage is all about treble, open air flow, timing, and phase. Since the phase really should not be played with in a headphone because it is drastically altering the sound we are left timing, air flow, and treble. Treble is important because we gather our positional cues from treble rather than bass because treble has much shorter wavelengths making it easier to pick out where the sounds are coming from. Bass has longer wavelengths and this leads to it confusing our brains as to where the sound is coming from. Both the HD650 and X1 are weak in the treble leading to a limited soundstage. Good air flow helps because in closed headphone the driver can sometimes have unwanted resonances, reflections, and damping. The same can happen in any headphone really, but closed headphone are tricky to due well because of the lack of airflow into the aircup compared to open headphones. Another factor to consider is the angle of the drivers as this plays an important roll in coupling the headphone to our ears. Everyone's ears are different and thus have different idea positions / angles for headphone drivers. As the sound enters the ear and takes reflections off of its surfaces the sound changes. If the angles are not ideal the soundstage along with everything else will suffer.
You can read a little about phase here:
Phase:
https://www.youtube.com/watch?v=bWB5PSoV2I0
One thing I always look out for is when someone claims that a headphone has huge soundstage. Typically this means there is some serious phase issues or incoherence between the two drivers giving the effect of having a large soundstage but in actuality is drastically altering the sound in a bad way.
A method also used in audio to increase the soundstage is to play with crossfade which feeds part of one channel into the other. This acts like a reflection in the real world because outside of the headphone sounds bounce off of objects and have different timing to each of our ears. This helps our brains interpret soundstage.
You can check out an audio mixing video that shows one example of altering soundstage with mixing:
https://www.youtube.com/watch?v=xDnsgvYwkIs
Some amps and DACs can mess with soundstage because they often have filters which affect the soundstage. There can even be phase differences! You have to be careful when a piece of gear advertises that it makes the soundstage huge because is it really being neutral or introducing flaws into the music. It might be more pleasing to listen to, but for many we like to hear what the artists and engineers had in mind when the first made the track.
My guess is headphones that have very large soundstages there is probably going to be easily measured volume differences between the drivers thus simulating a larger soundstage. Headphones that are more closely matched are going to represent the original mix more accurately.
Soundstage is tricky because our ears are different, every headphone is different, and even the mixes are different.
Have you tried listening to your HD650 without the foam inserts inside the earcups? You can easily remove it. Might help increase the treble.
Here is a thread that talks about various headphones and their soundstage:
http://www.head-fi.org/t/593365/the-soundstage-head-club
