Hmm, I knew it did that when the REPL wasn't on, because it gives very limited completion options compared to CIDER. Does Cursive even do this when you have access to a REPL, or when nREPL is running? That's the main reason I still prefer CIDER + Emacs, because it has much more useful completions, though still not as good as IntelliJ's completions for static Java code (only possible because Java is static).

Generally Cursive's completion should be (at least) as good as CIDER's, and if it isn't that's a bug I'd like an issue for. No-one has complained about it so far.