The main difference (as someone who is familiar with nginx and caddy, and whose Apache knowledge mostly comes from the era of "webapps are folders in your root with PHP files in them", so not very good) is that Nginx tends to be a very hands-off webserver. It doesn't do anything for you that the config files don't specify it should do. Of the three main ways to serve web content out there (static, CGI-esque aka PHP or a reverse proxy), nginx only really has a near config free experience (as in, your distro probably shipped a default config to make this work with zero effort) for serving static files - you just make a server block, a location block and point the root to the folder you want to serve. Setting up PHP or reverse proxies requires a lot more manual work; if you want X-Forwarded-* headers, you're gonna have to set those up for example.

Similarly, nginx isn't going to be the one picking your SSL config out of the box; it's a bunch of arcane flags and settings (if you're not intimately familiar with SSL anyways) that you look up once how to get the SSLabs A+ score and then you put it in a reusable snippet to not have to think about that stuff ever again for future domains. If you want ACME certificates, you're gonna have to tell it to do that (nginx recently got a module for this I think, which kinda makes it equal in this sense to caddy's automatic LE cert generation) or where to find the certificates.

Caddy automates a lot of this sort of thing; the result is smoother/cleaner config files (it's hard to deny that reverse_proxy is shorter than the several dozens of config lines you'd use for nginx) but you also need to be aware of what Caddy does by default and the assumption that what the Caddy developers think should be the default will also always be what you want, unless you want to poke at manual overrides (in which case it's pretty much nginx again.) It can also do a few common variants on static site hosting, like automatically pulling a git repo, running a page generator on it and serving the resulting folder, which nginx just straight up doesn't do afaik.

In practice, I found Caddy works well on development/toy machines where there's no real expectations for having to think about prod and "not having to spend an hour reconfiguring your setup" when you start a project is beneficial and it's easy to swap things like ports around. Nginx works better on production machines because you basically set it up once and then can safely never have to think about it again, while still allowing you explicitly see why it's (not) doing what you want later down the line.

Traefik I legitimately couldn't see a reason to use however. It's config syntax is atrocious and looking it up online tells me it's mainly popular with non-technical homelab people because it can serve a web UI to manage your reverse proxies in. I guess that's a desirable feature for some?