localstorage is just as vulnerable to being read by JavaScript as cookies are.
localstorage can be read using JavaScript from the same domain, if you control all the JS on the domain, then this shouldn't be a problem. But if any other code is executed (via injection for example, or if you share the domain with someone else), they will be able to access the storage data.
This is the same for cookies however, but typically the cookie is set to HTTPOnly so JavaScript cannot read it.
In either case, plain-text login information shouldn't be stored in either cookies or localstorage anyhow, as if someone does get hold of them, they can continuously make a new session for themselves.
You should encrypt an authenticated identifier (such as their user ID) along with the datetime of the session expiration, and then store this value in either a cookie or local storage. This token is then validated on each server call.
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