I think if we look at the historical averages we'd find that the average weights of rapiers were mostly the bottom end of average for the longsword. If memory serves the average rapier was about 2lbs, and the average longsword was more like 3lbs. Is that what you meant by close? I think that's a pretty big difference. I wasn't talking about a small sword - those are indeed smaller though, as the name suggests.
As for style, the Rapier is pretty universally acknowledged to be suited to nimble thrusting attacks, and only in a very secondary role as a slashing weapon compared to the longsword. The idea that more strength is required to fight one handed isn't entirely off base, but I think we might want to broaden our discussion to be more about what DBW terms 'melee' rather than a duel, since we're at least trying to use this in terms of D&D. Also, one handed fighting with a longsword was an integral part of at least some schools, more common in the Italian schools than the German. Also, the overall usefulness of thrusting, as far as those schools go, indexes pretty clearly to use against opponents in plate armour, which pretty much ignores slashing type attacks.
Since we're talking about D&D here, maybe we should be talking about both one and two handed play, since that's how it's written up?
15th/16th century rapier is as heavy (2,5 to 3 lbs.) and as long (4-4,5 ft. blade length) as a "long sword" as in 1 1/2 hands aka bastard sword. the point of balance is far more to the hilt than a long sword.
They are so heavy that you eventually want some additional means to parry: main gauge, a buckler, a cloak or a thick gauntlet.
The bastard aka longsword was used 1 handed on horse / with shield but normally two handed (no need for shield since sophisticated plate armor was available, so it was more important to use halfsword techniques to achieve some damage and combined sword / wrestling moves to topple the opponent in armor).
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