Is there a recommendation of what Identity Store (cookie vs local storage) to use?

In the Browser 2.0 SDK it says this:

identityStorage

string. Sets storage API for user identity. Options include cookie for document.cookie, localStorage for localStorage, or none to opt-out of persisting user identity.

By default this is “cookie” but is there an advantage to use localStorage?  When should we use this option? I realize there must be legacy browser issues, but that would have to be super old browsers that don’t support localStorage so trying to figure out the gotchas here.

The docs do not give any guidance on this.