If you do any kind of on-device work, it will spin up a local HTTP log server, and pipe logs from your real device (phone, hardware, etc.) to the server and do realtime debugging.
Claude will mostly guess, have you copy + paste logs, etc.
I’ve never used cursor and have only seen it in a couple work lunch and learn demos. I’ve never seen that feature. I have a lot of use cases where I’m asking cc to move a widget down a little bit or make a data table full width etc. Being able to reference the actual UI would be useful.