The GS-X is a capable-enough amp for most current dynamic headphones, short of orthos/planars of course. The headphones you own shouldn't pose any struggles for the GS-X.
I wouldn't personally recommend it over the GS-1 for most people though, as the GS-1 is essentially the exact same amp, just not balanced. IMO, to get the most benefit from the GS-X it should be used in balanced mode (which also requires a balanced source, as the GS-X is a proper dual mono amp without phase inverters).
There's only one reason I'd recommend the GS-X over the GS-1 excepting the balanced functionality - it's marginally more "transparent" sounding and will reveal everything about the source it's connected to, which will provide more benefit on very high-end sources.
Most people on Head-Fi seem to look at amps as some sort of "tone control" - completely the opposite of the HeadAmp amps that I've heard. HeadAmp amps sonically disappear and are the most literal "wire with gain" amps that I've heard to date, with the GS-X being the best at that. It really takes on the character of the source it's connected to - I've done plenty of digital source comparisons (both with my 1st GS-X in 2007 and the one I currently have which I got in 2010) and heard surprisingly different sounds with each source.
The GS-X is my highest recommendation only for people with (preferrably balanced) high-end sources looking to reap as much reward as possible. Otherwise it makes more sense to get the GS-1. If my description of the HeadAmp "sound" doesn't seem appealing, there are probably plenty of other amps with more "mid-rangey" sound signatures available. I'm not really aware of such other amps though as my experience is very limited.
My favorite GS-X experience by far was with my previously-owned balanced Sony Qualia 010. The total treble quality that my system created was absolutely and awesomely clean & pristine - the GS-X really enhanced the treble in particular and made it perfect for me.