Paladin vs Avenger

I have seen many walkthroughs and I have almost never seen anyone using the Avenger headgear to beat the very hard levels. I am currently at Cave 2, Princess, Paladin and Adventurer Pig is my go-to set up. Are there any scenarios where the Avenger headgear is more useful than the Paladin headgear, or is the Avenger just a poor man's Paladin? Also, does Avenger's rage chili damage increase as its health decrease?
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