The rivalry between the two popes is nothing worth mentioning. Kenneth is not even fit to carry Risa's shoes.
Kenneth has the Philosopher's Stone, and so does Risa, with more quantity than Kenneth. If it comes down to equipment, being both popes, the Heavenly Father's Court, possessing the top resources of the God-chosen Continent, can crush the Death Church with equipment alone.
Even without equipment, or rather, even if Kenneth uses equipment while Risa fights barehanded, the battle is still one-sided.
At the very outset, Kenneth was pressed to the ground and rubbed.
Kenneth wields the Philosopher's Stone, utilizing demigod-level power as a Legendary Mage. Risa is also a Legendary Mage, and without equipment, exhibits demigod-level power.
This alone surpasses all the powerholders of the Church.
Knowledge is power. Risa knows too much, and this knowledge gives him the confidence to challenge ranks.