The two are largely identical. The CHB has a four-pin headphone connector that also carries composite video, and therefore defaults to composite by default. It's also got a 44-pin header instead of an LCD connector.
On the inside, by default, they both have the same system software. There are a few checks in the kernel to detect which version of the board it's running on, and I seem to recall the only differences are in the 5-way joystick, the default video out, and some small thing involving needing to set a transistor to enable the battery charger (I can't remember what, exactly.) It's also got more USB ports.
If you want composite-out on your One, it's literally a two-wire solder job. One wire if you feel like using an alligator clip to find ground.
Seeing as how the CHB is just a naked board, it's obviously much easier to get to the SD card to replace it!