Did Rabbi Ovadia Yosef respect him as a big person in Torah? And does he ever bring him down in his halacha books? and where?
Rav Ovadia’s encyclopedic memory was based upon the myriads of books which he swallowed and remembered, not on current halachic responsa issued but not published, which was most of Rav Goren’s writing during his lifetime (his early sfarim don't deal with practical halacha). Accordingly I didn’t find Rav Ovadia citing Rav Goren. They had a mutually respectful relationship during their tenure as rabbis of Tel Aviv, but not during much of their time as Chief Rabbis of Israel, until towards the end, when they made peace (Rav Goren even asked his wife, before his passing, to have Rav Ovadia eulogize him, which he did). Rav Ovadia also always agreed to give Yahrtzeit Memorial Lectures dealing with the Torah of Rav Goren.