I've not used an H2, but the demos I have seen pretty much are punch a button and play. Then punch another button to play it back, or hit a few buttons on the screen to upload. The H4 came with a 100 page manual that was pretty much unintelligible (to me anyway). I mostly figured out how to use it by pushing buttons. Now, that I know how to do it, it really isn't that complicated, and the manual almost makes sense.
A lot of the complication on the H4 comes from the fact that you can use it as a simple stereo recorder - pretty much push the button and record, but you can choose 50 different input filters for different amp simulators, reverb, etc. You don't have to mess with that if you don't want to. In addition, the H4 can also be used as a 4 channel recorder and the way you record each channel is not exactly the same (i.e. you push the buttons a bit differently), but again you don't have to use that feature. You can also choose to record from the built in stereo mics or you can use the 1/4" jacks to plug your guitar/uke/drum machine or what have you into it and you have to tell it what you want to do. There is more that you can set on input levels, etc etc, some of which I have still not used. Selecting many of these functions is very non-intuitive at first. Until you get it, it makes it complicated. I think they learned from the H4 and removed a lot of that to create H2, which is probably all most of us need.
You can also use the H2 or H4 just as a set of stereo mics, but you can chose reverb and amp effects or just feed it clean. I seldom use the H4 as a sort of tape recorder , the way I see guys like Ken Middleton doing. That is mostly because I usually record in the same place and don't really need a remote unit recorder. The H4 eats AA batteries pretty quickly, so I like to keep it tethered to the wall.
There was a thread not too long ago about a recorder and mixer that I thought looked like it would be very intuitive. It was the Teac DP-008, which is an 8 track mixer, recorder, with built in high quality mics. I don't know how its sound compares to the H2, but on YouTube it sounded good. There is a 4 track version DP-004. I kind of liked it because you set everything with knobs, so even I could figure it out easily. The 4 track is around $130.