It's also worth remembering that the Classical and Medieval pike doctrines evolved in very different contexts. Jus to point out the obvious difference, the former were essentially a mobile wall whose (original, anyway) purpose was to pin the enemy center in place for the cavalry to flank and destroy. The latter, conversely, was developed by a confederation which for most intents and purposes had no shock cavalry, and had to more or less depend entirely on their infantry for victory.

Similarly, while the Classical phalangites fought in a long but comparatively thin line and were severely vulnerable to flanking should it become disjointed, the Medieval and later pikes operated mainly in huge rectangular "living fortresses", with integral missile and close-combat support troops, that could fight in all directions if need be; the Swiss at least usually deployed three en echelon, so that the "main" and "rearguard" squares covered the flanks of the vanguard formation.

Regarding the "close assault" troops used to create holes in pike lines, AFAIK the two-handed sword stopped being an effective pike-chopper chiefly because everybody started unsportinly adding long metal strips (usually called "langets", IIRC) to their pike-shafts as a reinforcement...
Anyway, the standard kit for such "assault infantry" was a mixture of big swords, polearms, swords and shields and - rather importantly - good armour; AFAIK "three-quarters" plate (that is, full body and arm defences plus the upper legs) was common...
Quite a far cry from what the warriors of Antiquity had to make do with, obviously.

Proper knights and men-at-arms, of course, then sported some of the best defensive gear mankind has ever devised (before modern times anyway) and when dismounted were often a very serious headache for even the best pikemen. I've also seen references of 1500s French Gendarmes - arguably the apex of the European "heavy lancer" concept - in fact on occasion having been capable of punching a lance charge right through a Swiss square, although to no great effect as the blighters just closed ranks over their casualties afterwards...