rust-analyzer currently only support VScode officially. It may replace rls in the future, if it does it will probably support more editors too.
I used IntelliJ in the past for a long time. It's really a very good IDE and integrates well with tests, package version suggestions and generally feels more complete. I moved to rust-analyzer because my laptop started running out of resources and VScode was more responsive, it doesn't have intellij's nice extras (tests, dependency management) but the code completion itself is very fast and generally works better in some cases (such as my own).
rust-analyzer gets updates very often and just gets better every time, it wouldn't hurt to give it a try.
I‘d say that IntelliJ and rust-analyzer are comparable these days, and that there‘ probably little reason for switching if one is happy with IntelliJ.
This is probably more of a difference between editors, than between Rust plugins, but I’d say that IntelliJ generally has more convenient small things done right, but VS Code is faster to start up (but still is much slower than emacsclient ).