If you were where it was cold enough for frozen metal to cause a problem, I'd recommend wood. In Los Angeles, I don't think it matters. On this site, you will see where people successfully use about anything under the sun as a nest box. I'm sure some of them live in the frozen north and use metal successfully, but I'm an engineer and overthink and overplan by nature and training.
I've seen where some use a removable insert to make cleaning easier, like a plastic tub or a cut-down cardboard box. Just lift it out, dump the contents, clean or replace it, replace the bedding material, and put it back. Whatever you do, you need enough bedding material to give the egg a soft place to land, cuts down on cracked or broken eggs.
As far as cleaning after a broken egg or to remove chicken poop, I don't think there is a lot of difference in cleaning between wood and metal. Mainly remove and replace the bedding.
Personally, I just like the way wood looks, at least after it weathers. It has a nice comfortable look to it. Purely personal preference.