hugelkultur question.

I'm going to make above-ground beds and if branches and wood are good, wouldn't wood chips be even better? They are more broken down already.

Better and worse are subjective judgements based on your goals.
The benefits of full logs/branches arise from their being less broken down. It lasts longer, holds more water, less surface area means it ties up less nitrogen, more stable environment for fungal communities. Plus, you don't have to expend the energy to chip them up

Wood chips offer some.advantages for use on the surface where the feed soil life more readily, spread evenly and more attractively (to most peoples preferences), and create an easier walking surface.

I think there are benefits to having materials of different sizes that will break down at different rates. So i start with larger branches and stumps and use smaller branches to fill in gaps and finally pour in woodchips to fill in the cracks.