As someone who's used a number of swords (I'm no expert, but I have the proficiency

), there are clearly limitations on what you can do effectively with a large sword.
There are arming swords - think a viking sword, a knightly sword etc. These have a short grip that fits one hand and that is it (btw, this makes the sword harder to disarm - a long handle sticking out can be a weakness). IMO this is a D&D longsword that isn't versatile.
Then there is the "hand and a half sword" - a sword with a slightly longer blade (inch or two at most) and a slightly longer handle. It can be swung with one hand quite well but the handle can accommodate a second hand fairly well, although frequently this hand will grasp the *pommel* to get superior leverage. This specific sword is the one I'm most familiar with and used fairly frequently:
http://casiberia.com/product/albrecht-ii-hand-and-a-half-sword/sh2034 (I have the "practical" version of this which is very blunt for safety reasons).
another example:
http://www.albion-swords.com/swords/albion/nextgen/sword-medieval-mercenary-xva.htm (would *looove* this one).
I think hand and a half sword really represents the D&D longsword.
After that... well what is a greatsword? Well that gets complicated.
You have the "historical" longsword, which is a lot like a hand an a half sword except the blade is a few inch longer, but the main difference is the handle is a lot longer. This allows the user to put in a *lot* of torque (ie leverage) and deliver powerful and *very fast* blows. It's also an excellent defensive weapon.
http://casiberia.com/product/tinker-longsword-sharp/sh2394
http://www.albion-swords.com/swords/albion/nextgen/sword-medieval-munich-xviiib.htm
As far as I know, Dd&D doesn't have this specific weapon.
Can this weapon be used one handed? Yes! But not as well as an arming word or a hand and a half sword. While the hand and a half is made to optimize both style of fighting (ie, the "bastard" sword), the longsword is clearly optimized for 2 handed use. Still the blade is not so long or heavy that a one handed strike is impossible.
Finally, we have the D&D "greatsword", an enormous blade that just is too big for 1 handed use. This includes things like the larger claymores, the zweihanders etc...
http://casiberia.com/product/lowlander-sword/sh2065
This beast was owned by a friend of mine who was *huge* - he was 6'5" and very strong. I can't even handle a blade this size. Even for him, swinging it one handed would have been almost impossible. I believe that such weapons were designed for very large/strong men
SO. Based on this, greatsword swinging is impossible (and we really miss the "proper" longsword)... BUT.... well historically sword produced were on a spectrum. What about a two handed sword not for my giant friend but for a slightly tall guy like me (5'11")? Like a more reasonable claymore?
http://casiberia.com/product/claymore-antiqued/sh2060n
or something like
http://www.albion-swords.com/swords/albion/nextgen/sword-2hander-archduke.htm
I could use this two handed (although not with the speed of a longsword). Should it have the stats of a greatsword? Probably. Is it swingable with one hand? I don't know...