A devotion paladin, an ancients paladin and a paladin of vengeance walk into a bar. What do they fight over?

I'm writing an adventure for paladins with different backgrounds who are very similar on paper, but will find in reality traveling together will challenge their beliefs and forge them into stronger, more thoughtful, champions. I'm having a lot of fun building temples and shrines to different gods and communities and interesting npcs based on those faiths, but when it comes to the oaths there is some significant overlap. It seems like these paladins wouldn't disagree until SEVERAL rounds of drinks and then asking, in detail, why they made ultimately the exact same decisions. It seems like vengeance would be the easiest to tempt, but even a vengeance paladin piloted by reasonably intelligent player isn't going to do anything to noncombatants. I'm planning on writing a conquest paladin with loose morals to be an antagonist that they will be motivated to actually throw down with, but I don't know how to challenge this group with these tenets.