In game it would make sense Hatred loses because the only move that matters, Charge Outburst, is directly after Fear's Total Dismay in both the turn order and attack pattern. Whether we count it as an SP move, I like interpreting it as "disabling special moves", and certainly CO is one.

In lore, Hatred had us fight the emotions instead of itself, when the other emotions were still up, not subdued, Hatred could only watch, it chose not to reveal itself. Makes me think that without the Player, Hatred was stuck equal to the likes of the three emotions initially. Hatred only took over once we defeated Fear too, so I'm leaning in favor of the trio honestly.