The crucial aspect is absorbency, and the key to absorbency is surface area. The smaller the size of the cover material, the more effective it is at soaking up moisture and odours.
This is why sawdust is so amazing at doing this job. Tiny particles of wood soak up a large amount of moisture and odour. A little goes a long way.
For various reasons I recently changed from using sawdust to mushroom
compost. And I've noticed that I'm using more mushroom compost to do the same job as a smaller amount of sawdust, due to mushroom compost being larger particles with smaller total surface area.
Wood chips I imagine would perform this job more poorly. They are better suited to covering the humanure contents once they're dumped in their final position completely absorbed into their cover material.