As others have noted, slopes are a huge killer, and heavy cavalry or FMs will disrupt your phalanx to the point where they get slaughtered while trying to reform. I've also noticed that even small stat differences (as you saw in the 2-point advantage) seem to get magnified in phalanx duels, possibly because they just last so long. Presumably this applies to general's stars as well: if you're fighting at a disadvantage there, then your phalanxes will be minced.
Overall, I never trust my phalanx to win a duel, and my Successor battle always turn into a race to get around the rear of the enemy phalanx. Even then the enemy phalanxes typically take a long time to die against flanking infantry, so I try to do an alt-right-click heavy cavalry charge into the rear of an exhausted unit for a quick kill. Generally I leave the cavalry in the charge, take my phalanx off phalanx mode and tell it to alt-right-click attack as well: the enemy phalanx ends up crushed in a scrum, where they're busy trying to reform but are being cut to shreds by heavy horsemen from behind and suddenly-agile opponents from the front. Since phalanxes are almost always disciplined, inflicting sudden massive casualties in this way is the only way to break them. If I could be bothered to wait, the other tactic would be to flank with infantry with lots of javelins, and throw them ALL into the back of the phalanx before charging into hand-to-hand combat.
For most battles I size each phalanx to be 6-deep, so it can take some casualties and still present the full 5-deep wall of spearpoints. If you're doing lots of maneuvering (e.g. in cities), then they'll default to moving in a roughly-square formation. If you let them move like this and leave guard mode off, then when they hit something you'll see them switch to a slightly wider and shallower formation.
Canceling "fighting" status by hitting backspace will reduce the rate at which you kill the enemy now, in return for saving energy. Then when the enemy is exhausted your troops are still fresh, and can hopefully take some revenge.
Another tactic which I've never tried but MIGHT work would be to keep refusing your entire battle line: whenever the enemy phalanx lowers its sarissas and starts marching, back yours up (out of phalanx mode). The goal is to exhaust the enemy phalanx before combat starts, which will greatly reduce the rate at which they kill your guys, and make them easier to rout when charged from the rear. Obviously only works if there are slopes and/or stat-heat differences involved
The "refusing" tactic can also be a way to break a battle line that's too broad to flank: as the two phalanx lines advance, let one of your center units stop. Typically the opposing unit will keep coming through your lines to make contact. Now you can attack it in safety from the flanks, because it's behind your lines. And once you've routed it, you have a hole in the middle of the enemy line to feed troops through.
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