The only thing the BR has going for it are it's "effects", which the H2 has none of. If you're an acoustic guitar player like me, that feature is not very important.
The "only" thing??? Absolutely not! The Zoom H2 is a simple 2-track recorder, while the Micro BR is a multi-track recorder with 32 v-tracks, built-in programmable drum machine, and much more. And, by the way, some of the Micro BR's effects can be quite useful for recording acoustic guitar. In fact, a few of the preset patches are designed specifically for acoustic guitar.
The H2 is simply much easier to use.
If you use the Micro BR as a simple 2-track recorder like the H2 and ignore all its additional features such as virtual tracks, effects, and drum machine, it is just as easy to use. Because the Micro BR has more features than the H2, it requires a bit more effort to learn how to use those features.
For instance, with the Micro BR, after you stop a recording, in order to play it back you have to "rewind" it first as though it were a tape.
Not true. Pressing the STOP and REWIND buttons together instantly resets the song to the beginning.
I'm sure the H2 is very handy for recording interviews, seminars, rehearsals, etc., but it can hardly be compared to a multi-track studio like the Micro BR. The H4 comes a bit closer with its 4-track mode. But it lacks v-tracks and a drum machine, and costs considerably more than a Micro BR.