The primary difference between the traditional conductors and advanced conductors is temperature tolerance. Most transmission lines are aluminum conductors with a steel core for strength (ASCR). As current increases, so does temperature, causing lines to sag (or the steel anneal if too hot).
Advanced conductors use a different composition to operate at higher temperatures, or otherwise carry more current (one example: aluminum conductor, composite reinforced, or ACCR) so as to have similar weight (and profile) to the original, traditional conductor.