So sorry, I missed this post earlier.
To answer your question I got both out just now and am doing some A/Bing. I'm a recording engineer and producer so I have to express what I'm hearing in the terms I think in which is more musical than technical.
To me, the H2 grooves harder. In the biz that means grooves (the heart of the rhythm of a track) get under your skin more and draws you in. The technical reasons this is happening that I'm hearing are that 1) the H2 bass is tighter, meaning downbeats are more clearly defined (H1's bigger sub bass smears bass transients a bit in comparison). 2) The the H2 is less "sparkly", meaning that the highs flow more smoothly out of the mids (they sound like part of the same sound that's generating the mids, which is of course what's happening in reality). The H1 has a more clearly defined "treble" to me (as does nearly every other headphone I've ever heard). The listening result is that the instruments get more punch and your attention doesn't get pulled away by the highs.
The H2 brings all that tactileness the H1 has (that sense of kick drums really pushing real air, guitar amps vibrating, etc). To me it's more like listening to a live performance than other headphones are (less emphasized highs and lows but a real solidity to the sound).
Of course, different people have different tastes, and mine runs to really loving the coherence the H2 brings. Others will miss a "wow" factor like the bass in the Empyreans (however you spell it lol), or the pristine highs of the DCA Stealth.