When the wood block is dropped in the water and settles so that it floats and is no longer bobbing up and down, how do the buoyant force and gravity compare?

When the block settles and stops bobbing up and down, the buoyant force and gravitational force on it must be EQUAL.  If they were not equal, then there would be a NET vertical force on the block, and it would be accelerating vertically, either up or down.  It's not, so there isn't.