What features of a stack exchange site - connected to content display and moderation rules - can be decided on and implemented on a per-site basis?
Is there a public, central comparison anywhere of how each community has chosen to set them up?
This is a little broad, so the best I can offer you is a general rule of when something is probably configurable per-site. I want to offer that with a healthy disclaimer:
Just because we can configure things differently per-site doesn't mean we should or will.
The following things are common to be just a little different from site to site:
Other things are sometimes changed depending on the volume and needs of a site:
Everything else remains pretty much the same, with very few exceptions. The goal is to provide a familiar interface to a wide variety of topics and communities - the software being the middle ground.
Most settings are established based on the Area 51 proposal and outcome of the private beta period for a site, it's more what a community shows than chooses, although they definitely have say in the matter as expressed on their meta site.
This isn't something that we'd really showcase, it's just plumbing, and I'm not going to go into it more - but there's no harm in listing it, so here it is :) This is not meant to be exhaustive.
1 Internationalization makes this interesting, on non-English sites, copy changes are a bit more of a big deal.
(I don't know if such a list exists elsewhere. I like the idea and I made this CW so that the list can grow.)