With claude, the difference I noticed is that you can run their cloud enviroment from GUI app, as well as connect to remote machine. Sure, remote connection is nothing interesting, but I'm not aware if claude cli can work with cloud based enviroment. Also claude design is alvaliable on claude gui app. But all of these can be accessed with the browser as well, only the local machine access is something that browser version doesn't have. But for that you can use cli... Really mess of the tools they are shipping. Waiting (not) for Claude/Openai OS