According to the Gaudiya Vaishnava tradition, when Sri Chaitanya was in Varanasi, he defeated Prakashananda Saraswati, the famous Vedantin. Showing this event, Vaishnavas claim that their philosophy is superior to Advaita Vedanta.
My question is, who is Prakashananda Saraswati? Was he an authority in Advaita Vedanta? Did he belong to the Guru Shishya lineage established by Shankaracharya?
If he is not, then by defeating a random guy, somebody cannot claim the superiority of their school.