First of all - what do you mean state ? In redux - state is just a plain object (plus some methods, but still). So when you read data from there - you just read props from object.
While cookies, localstorage - it's DOM api, which first of all slower, plus you need not only read data, but also parse it (cause both cookies, storage work with serialized data). So definitely storage/cookie slower than state.
You can check http://jsben.ch/nvo5G
BUT! - you can't save in-memory object state between page reloads. So for this, you can use storage (pattern named persistent state. And there is probably no other way to implement this functionality (or client DB) - in case you need to restore some state on reload - you have just two options - save state on a client (cookies, storage/db), or on server (and do fetch request).
It's MICRO optimisations, mostly you shouldn't care about it (in the case of reading just on start app)