Here are a couple of other possibilities that might be worth considering…They are a bit more expensive than the ones you listed, though (~$100 more).
The first is the Oade Concert Mod PMD620. Sounds awesome, in my opinion, and has an uncluttered layout (both physically and on the screen), nice tactile buttons (and one-touch recording), sufficient plug-in power for most small mics, decent build quality, very good battery life, and an interesting preset system. Downsides are that Oade removes the built-in mics (which may or may not be an issue) and the modification voids the factory warranty.
The other is the Sony PCM-D50. I have had a few opportunities to play around with one, and it is pretty sweet. Very solid build and it sounded great in the home tests I did with it (but I have never recorded a concert with one). I have read a lot of positive comments from people that own/use one, and, although bigger than the others, it is not as big as I thought it would be (definitely “low-pro”-able). Also has decent plug-in power, optical in/out, built-in memory (4 GB, I think), and excellent battery life.
As for the H2, well, in my opinion, any of the above would be a step up! On mine, the mic input was pretty noisy, and I didn’t like the gain control (or lack thereof)…