I used 1/2" hardware cloth on the bottoms of my lower row of nests. My higher nests are wood bottomed. My nesting material is dried grass that I gather from places I don't mow or weed eat and spread to dry. Really close to hay. A lot of broody hens have hatched in both types of nests.
I've read various reasons you might want a wire bottom. Supposedly they are more flexible than a wooden bottom so eggs are less likely to break. I'm not impressed with that logic, I use wooden bottomed nests higher up and the eggs don't break in those either. It might make a difference if you didn't use any bedding but that is not my reality.
It's supposed to keep the nests cleaner, the dirt falls on through. That's part of why I did it. But I don't see dirt or debris building up under the nests. The "hay" I use for bedding is somewhat delicate and gets scratched into tiny bits but the other hay catches it before it goes on through. When I clean the nests out, which is generally after a broody hen hatches, the wire bottomed nests are marginally easier. In either case I have to remove most of the bedding by hand. The only difference is that with the wood bottomed nest I have to work harder to get the fines out (if I want them out, often I don't see a need) while with the wire bottomed ones I just have to rake them over the wire. How much time does this save, a whole minute or maybe a minute and half. To me that is negligible plus I hardly ever do it.
As far as cleaning out a broken egg, the nesting material acts as a diaper and soaks up the liquid. I generally just have to remove a handful of bedding. I don't see any real difference between wire or wood bottomed nests. If you don't use bedding I'd prefer to clean wire than wood. At least a lot of the liquid would drop on through.
One reason I used wire was that I hoped to get better ventilation in the hot summers. I don't want my nests to become an oven. But the "hay" nesting material pretty much seals the bottom of the nest so I don't think there is any advantage there.
Having both so I can compare, I really don't see any real difference in either they way I do it. If i were trying to use something like sand for a nesting material well duh! Using 1/2" hardware cloth I'm not sure how many wood shavings would actually fall on through. I tried that once, wood shavings, but prefer the "hay" as it is cheaper. 1" hardware cloth might make a difference there.
There probably are specific applications where one is better than the other but I have not seen them the way I do it.