I'll also add that there are some S+S infantry that should be a decent fight as some faction get high end S+S instead of 2H.
And High End Sword and Sheilds will beat low end 2-Handers, Also, those that don't get 2-Handers tend to get Good cav, Pikes, Insane Foot Archers, or HA. Everybody gets some sort of counter to them.

I think their armor is too low, actually, or the swordsmen's defense is too high. A swordsman can exceed 20 defense, with a whopping 8 defense skill plus a shield bonus of 6 added to his base 7 for heavy mail. And he can usually get further upgrades to his armor while retaining all those bonuses intact. A 2hander in advanced plate (no more upgrades for him) is lucky to get 14, with around 4 defense skill. His advanced armor only gives him 3 extra armor over what swordsmen start with, slows him down by four or more points of defense skill, and makes him pigheaded enough to do without 6 points of shield. Given how many AP missiles and melee troops are flying/running around in M2TW, 2handers tend to die rather easily. Plate armor made shields unnecessary, but you hardly see that in the game atm.
The thing is Dopp. Even non-Ap missile where meant to present a serious threat to 2-Handers, it's one of the mechanisems by which they've been made balanced in spite of their insane melee skills vs. other infantry. Also, Sword and Sheild units get such high defence to help them at least do some damage vs. 2-handers. 2-handers are supposed to hurt, but not have a free lunch. I find the best S&S units can inflict about 25-30% losses on 2-Handers before dying.

Swordsmen also have ridiculously high defense skills just by virtue of carrying swords: 8 or 9 compared to 4 or 5 for most infantry (and 1 or 3 for anyone carrying a spear). All this generally means that earlier units are better protected in melee than later, more heavily armored units, by an enormous margin, great enough that even when the AP is factored in, DFK are actually still slightly better protected than DGK (and actually, vanilla DGK don't have AP at all). So far the shield bug has kept sword and board men from showing their true potential, which leads me to wonder if they were given such high defense skill to compensate. Perhaps it's not necessary any more with the shield fix in place and they should be dropped back to 5 defense or something.
Perhaps. However I think a lot of the bugs got introduced between the two demos TBH. When they changed some of the 2-Hander animations around I think they rebalanced all 2-Handers on the spot, which explains why Halberds and SHS are so weak compared to fixed 2-Handers. (Intresting question, did the stats of 2-Handers go up at all between the 1st and 2nd Demo?). If the Sheild Bug crept in around this point or not would tell us how they might have intended S&S to perform. But to me, seeing DEK rip through Dismounted Christian Guard with about 30% losses is OK. Any better and I feel 2-Handers would risk become the new cav. Somthing that only Pikes can stop.

It's all relative to the unit itself. There shouldn't be clear cut stone-scissors-paper. Some of the decent 2 handers (like dismounted english knights) should be able to crush most infantry. While some should get torn up by decent swords.
Indeed, in fact thats exactly what happens, the best swords can beat the weaker 2-handers whilst the best 2-Handers only get beaten by Pikes, but can be made to take modorate, (25-30%), losses in the process of winning.

I think most people view double handers as higher attack, lower defence. Something to smash through infantry quickly, yet lack the staying power of more armoured units.
Thats an OK description of them, they can and will beat any non-pike infantry who attacks them, but without getting the charge they suffer much heavier losses.