Firefox ESR is basically the LTS of Firefox. Over a portion of the normal ("stable") Firefox's release cycle, ESR will get security fixes and backports, but nothing that changes interface or expected UX behaviours. It's basically there for keeping an environment that is consistent and predictable over a reasonably long term (~1 y) which is why it's the Firefox version that gets shipped with eg.: Debian.

In general, ESR is the default version I install for anything clients-wise that for some reason requires that we don't intervene client machines too much (including maintenance). It's fire-and-forget once you have the usual extensions rolling like uBlock Origin.

Memory wise it's also quite reasonable in its usage and I've found it's far more responsive to customization of in-RAM memory usage patterns than stable, nightly or develiper Firefox, who tend to ignore or misinterpret my requests such as "only use up to 16 MB of cache in RAM".

One part where maybe ESR is too conservative is the HTML / CSS lexer. Because it's intended to stay stable over very long periods it gets stuck with stuff like still not accepting CSS :has(), and it seems the next ESR won't support it either, whereas Nightly does already. Also, because behaviours are retained as long as possible, bug UI breaking changes such as the migration off Australis or the incorporation of the Extensions Button are a more jarring clash in ESR than in normal Firefox, because you get all those workflow-changing changes in one BIG update.

I use it on one machine because it's the only thing available there. I frequently have problems with web sites that refuse to work because my "web browser is out of date." Google, in particular, is bad about it, and even seems to actively user agent mocking from working. I know that's not FF's problem, but it is a severe issue that makes me wish I could update to a newer version.

Firefox ESR is an older version of Firefox that continues to receive security updates. It is made for conservative enterprise environments that care more about stability (as in: not changing) than features or fixes. It may or may not be more stable (ideally, newer versions would fix stability issues in older ESR versions), and may use more or less memory (regressions in memory usage should be reported).

I have tried it in the sense that I have a copy around for testing in those odd cases where someone is using ESR. I don't recommend it.

I use it because that’s what my Linux distro packages. It’s fine, but unless you’re averse to change there really isn’t any reason for a regular Firefox user to choose ESR over the regular release. I do occasionally get flagged by websites for using an out of date release, which is kind of annoying.