This is not really true anymore.
Cursor has better cloud agents than Claude. The multi-agent experience is better, the worktree management is better. Tagging specific code or files in chat is better.
It's hard for me to express the level of pain and frustration I feel going from Cursor to Claude / Conductor+Claude / Claude Extension for VS Code, Claude in Zed, etc.
Really hoping Claude puts more energy into Cowork as a competitor for Cursor and Codex.
Instead they are defining architecture through specs and verification-loops and attempting to one-shot solutions fitting clear tests. On reflection, I personally don't have many prompts with CC referencing files or code directly, rather I speak in specifications I can then track to a given instance of work in review.
This isn't to suggest you can't work at this abstraction in cursor or w/e interface, but the features you suggest are hardly relevant to the divide zwaps is identifying.
I'm not telling you to go use cursor, just to help clarify that you can drive both solutions with the exact same approach and skillset and get very similar results - the difference is the UI. I personally like being able to paste screenshots into the agent, etc.