How hard is the difficulty check for winning the argument (the number your opponent has on his side of the rock-paper-scissors interface that determines how many pips are filled every time they win a round) ?

I think the amount of XP rewarded would depend on that. For example, when you obtain the missing teleporter pyramid and have a verbal joust with the bathing mayor's wife, she gets 8 pips for every won round of rock-paper-scissors, where as the player gets 2. Obviously that's a very difficult argument for the player to win, requiring either a lot of luck or a significant investment in social skills on the player's behalf.

The latter is worth rewarding (and is, actually - you get a nice chunk of Charisma Experience if you win that argument). Where as Hiver suggested above that fighting all the warriors is "..not easy..", neither is winning the argument with the Mayor's wife. They are simply different types of challenges, requiring different types of investments, and this game goes through the effort of providing multiple paths through these challenges and tries to make social skills seem as important as fighting skills.

So, (again) it would depend on the difficulty of the debate with the Stone Warrior. If the odds of winning the argument are in the player's favor even without an investment in social skills, the reward should be weak to reflect that. If, however, they are in the Stone Warrior's favor and a healthy investment in Charisma is needed to have a reasonable chance, that should be reflected with a decent reward. If the odds of winning the argument against the stone warrior is slim enough, I can even see winning the argument being worth more experience than simply fighting the stone warriors. We shouldn't assume one route is the harder one simply because it involves combat and the other doesn't.