It's really a matter of preference. I use wood shavings, I like how they smell and they are easy to keep clean. I hate straw with a passion. I know some people think it's easy to clean up but I despise cleaning straw out of anywhere. Mine don't kick the shavings out of the boxes too badly, works for us.
ETA: And as a livestock owner hay in nest boxes just seems like sacrilege. That's FOOD, people!