I got an H4 from band funds before the H2 & H1 came out. Got good results from it, but its a bit plasticy and when recording a gig on batteries I have to remember to put a fresh set in between sets.
I think the main benefit of the H2 is that it can record 360 degrees - ie one set of mics pointing at the band and another set picking the audience (or tumbleweed) behind, or for an acoustic "living room" rehearsal with everyone on a circle it might stand a better chance of picking everyone up clearly in 4 channels rather than just 2.
As other band members use the H4, I'm thinking of buying one for myself. I really like the simplicity & size (& price) of the H1, but the 4 channel recording of the H2 is a massive bonus. Then again the Q3 looks temping at around the same price of the H2 - again only two channel but with video in additon to the high quality audio recording.
Also the H1 uses Micro SDHC cards, the H2 & H4 use full size SDHC