MI13's linked comment includes details about 'half swording' techniques - armour cannot be -penetrated- by a sword, so when fighting a man in armour the objective is to slide a sword into the gaps in armour (forcing a gap open with a stiff point if need be). Half swording provides the point control to do this. Men at Arms would not swing away at each other and hope that a strong blow would penetrate, so combat in armour wouldn't necessarily blunt a sword extremely quickly. One type of sword, the Estoc, was made particularly for fighting against men in plate armour. It has very slight edges and a thick, narrow cross-section - its 'blade' is essentially a long awl, and it has a very strong point. Here is an example

The most effective weapon against armour (after 1450 or so) is a gun. Depending on the type of gun, it is one of the only weapons that can reliably penetrate armour, though not necessarily from medium or long range. Before that, it would have been a strong crossbow, a lance, or a polearm like a pollaxe, halberd or bill - particularly if the polearm has a sharp spike , or the spike on the back of a warhammer. All of these would be better against armour than a longbow, and much better than a sword. For instance, Tobias Capwell notes that lances can deliver up to 300 Joules of energy in his tests, which is far in excess of the 60-130 Joules of energy that Williams quotes for a sword or axe blade. 2mm of steel plate (a rough average for a breastplate before 1520 or so) cannot be penetrated by 130 Joules (applied at a point like an arrow or sword point) at any angle of impact, while it can be penetrated by 300 joules at over 45 degrees. Now actually -delivering- that energy efficiently into a human body while charging from horseback is hard, but this is a simple quantifiable illustration of how much more powerful lances are than swords.

For this reason, the primary weapon of mounted knights and gentlemen at arms was the lance. The primary weapon of dismounted knights and men at arms would be a either a 'short lance' for infantry use (a spear) in the 14th century and in the 15th and 16th centuries a polearm, probably a pollaxe but perhaps a glaive or halberd.

However, the knight or gentlemen at arms would almost always carry a sword into battle. It was a secondary weapon, but it was useful against unarmored men, could be used against armoured ones in a pinch (see half swording, above) and easy to carry on the person. So while not their primary weapon, swords were nearly ubiquitous among knights and gentlemen at arms in the later Medieval battlefield.

Sources:

-The Knight and the Blast Furnace, Alan Williams

-Arms and Armour of the Medieval Knight, Edge and Paddock

-Medieval Warfare, a History , Keen, editor

-The Real Fighting Stuff: Arms and ARmour at the Glasgow Museum, Tobias Capwell

Here are past posts on the topic:

0. Plate Armor and Effectiveness in Medieval Age (https://www.reddit.com/r/AskHistorians/comments/2z7t3k/plate_armor_and_effectiveness_in_medieval_age/)
^(16 Mar 2015 | 4 comments)
^(General answer by /u/WARitter)

0. Why did Knights still use swords after the invention of Plate? Wouldn't the Mace become the more favorable and even "romantic" weapon? (https://www.reddit.com/r/AskHistorians/comments/1w4gbt/why_did_knights_still_use_swords_after_the/)
^(25 Jan 2014 | 100 comments)
^(Sword techniques against plate armor by /u/MI13)

0. Why did heavily armored knights fight with long swords? Would it not be more effective to tackle them and use a knife to gouge at areas with little armor? (https://www.reddit.com/r/AskHistorians/comments/1p9tq1/why_did_heavily_armored_knights_fight_with_long/)
^(26 Oct 2013 | 20 comments)
^(Movement in armor and general combat)

0. How did the sword become the iconic "medieval weapon" when other weapons of the time were either stronger aganist plate or had more reach with comparable damage? (https://www.reddit.com/r/AskHistorians/comments/3g4w5w/how_did_the_sword_become_the_iconic_medieval/)
^(07 Aug 2015 | 7 comments)
^(The katana and Japanese armor by /u/bigbluepanda)

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