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!

Awesome!  Does that mean I can use CHB's software on the C1 then? 

What's the 5 - direction joystick you're referring to?  I don't recall there being a joystick on either one...