For the choice there are multiple questions to be asked. How "relevant"is the data, is it shared across browsers, howl on should it live etc.
Cookies are bound to a specific browser. The lifetime can be set from "during this browser session" to some arbitrary date in future. This doesn't mean the lifetime will be reached as there are different events at which a browser might kill the cookies. If its only you and your browser this might work .. ut the list might suddenly be lost.
PHP Session storage is stored on a server and referenced by a cookie or URL parameter. It has a relatively short lifetime (by default 24 hours) as by default the session files reside in the /tmp directory a cleanup process (ie. on server reboot after power failure or update) might delete them. Still not persistent. (PHP session handling could be configured in a quite persistent way but that's ignoring the purpose)
So both probably aren't good. Alternatives? Yes there are!
HTML 5 introduces browser local storage for more data. That is useful to have nicer access to the data and more flexibility in usage. Downside is that this still depends on using the same browser all the time and somecleanup miht free it unexpectedly.
A more robust solution is to use some server-side (PHP) script which stores the list in a database (or simple file) in a place where it is unaffected from cleanup tasks. By that the list can be access from different browsers (i.e desktop and mobile device) and won't easily go away.