I know there are a few different schools of thought as to how ancient greeks actually fought their battles (giant shoving match, "pulse" method, etc), but it seems like most theories revolve around the idea of a cohesive shield-wall, bristling with pikes being presented to the enemy and far fewer actual deaths than you'd think.
How did this change in the high middle ages as full plate armor became more common, shields became less common and weapons became more diversified (swords, pole-arms, maces, etc.)? To me it seems like medieval combat would be much more disorganized and frantic that combat between two ancient greek phalanxes.
Someone else will have to supply the answer to the Medieval side of your question, about which I know nothing. But I just want to correct the image you're giving here of Greek phalanx combat. As you say, there are two theories on how such combat would play out - but both would easily fit under the label "disorganised and frantic". Greek hoplites received no training and no formation drill; they charged into battle at a run, so that their initially regular rank-and-file deployment descended into chaos before they even reached the enemy. Some of this order may have been regained when the hoplites slowed down upon encountering the enemy line, but even so, their approach would have been uneven and their lines inevitably mixed up. Proponents of the idea of literal othismos (hoplite battle as a shoving match) then envision a brutal crush. Proponents of pulse theory argue instead for local duels and group advances and retreats all along the line. In both cases, violence would be confused, intense and deadly.
The following marvel happened [at Marathon]: an Athenian, Epizelos son of Kouphagoras, was fighting as a brave man in the battle when he was deprived of his sight, though struck or hit nowhere on his body, and from that time on he spent the rest of his life in blindness. I have heard that he tells this story about his misfortune: he saw opposing him a tall armed man, whose beard overshadowed his shield, but the phantom passed him by and killed the man next to him.
-- Herodotos 6.117.2-3
The Athenians now fell into great disorder and perplexity, so that it was not easy to get from one side or the other any detailed account of the affair. By day certainly the combatants have a clearer notion, though even then by no means of all that takes place, no one knowing much of anything that does not go on right around him; but in a night engagement how could any one know anything for certain?
-- Thucydides 7.44.1
It's often argued that the losses suffered in such an engagement were quite low, and even that this form of fighting was devised to keep casualties at a minimum. However, if the figures we get are representative, the opposite is true. John Dayton has pointed out that the losses suffered in the average hoplite battle (5% on the winning side, 14% on the losing side) are much higher than those suffered in many battles in Medieval and Early Modern Europe. Indeed, if we picture a victorious phalanx 10 ranks deep, their 5% losses means that half of the men in the front rank died before the enemy was driven off.
Setting shields against shields they shoved, fought, killed, and died. There was no shouting, nor was there silence, but the strange noise created by wrath and battle together. (...) Now that the fighting was at an end, a weird spectacle met the eye, as one surveyed the scene of the conflict — the earth stained with blood, friend and foe lying dead side by side, shields smashed to pieces, spears snapped in two, daggers bared of their sheaths, some on the ground, some embedded in the bodies, some yet gripped by the hand.
-- Xenophon, Agesilaos 2.12-14
We know nothing about the Greek art of spear or sword combat, since neither was generally practiced, and sources throughout the Classical period are conflicted over whether weapon proficiency training for hoplites served any useful purpose at all. However, a couple of traits are considered beneficial for hoplites - primarily strength, stamina and agility. It was assumed that the hoplite in combat would have to grapple with his opponent, but also to swerve, dodge, swing his shield, lunge and withdraw, and generally fight in the manner of a duel, presuming there was space to do so.
As to the devices introduced by Antaios or Kerkyon in the art of wrestling for the sake of empty glory, or in boxing by Epeios or Amykos, since they are useless in the business of war, they merit no eulogy. But the exercises of stand-up wrestling, with the twisting free of neck, hands and sides, when practiced with ardor and with a firm and graceful pose, and directed towards strength and health, these must not be omitted, since they are useful for all purposes (...) Wrestling of this kind is of all motions by far the most nearly allied to military fighting.
-- Plato, Laws 796a, 814d
[The Pyrrhic dance] represents modes of eluding all kinds of blows and shots by swerving and ducking and side-leaps upward or crouching; and also the opposite kinds of motion, which lead to active postures of offence, when it strives to represent the movements involved in shooting with bows or javelins, and blows of every description.
-- Plato, Laws 815a
In short, there seems to have been an expectation - confirmed by what little we hear of actual combat - that a hoplite would fight in a chaotic and lethal environment, a "storm of spears" in the words of Sophokles, where only his shield stood between him and sudden death. How different this would have been from Late Medieval combat featuring plate armour and polearms is a question I can't answer.