Storm Raven said:
What is the functional difference between an "epee" and a D&D rapier?
To answer that, one must first answer the question "What the $%^()&@#^)*&_@*$%^)*&^_(@*Y#*&$^&@%*&#% is a D&D rapier? The description says that it's a piercing weapon, but the picture in the PHB is of a $%)*!@#&%$(%*^&@%()Q@#(*% CUTLASS, a short, single-edge cutting weapon.
So, we'll presume that the artist was feeling more than ordinarily incompetent that morning and ignore the picture. Let's go by the description.
While the weight is not unacceptable in and of itself, it is confusing if compared to the "longsword". The D&D "longsword" weighs about a pound to a pound and a half more than it should, if the model is medieval one-handed swords, even in the era of heavy armor. But we'll pretend that this is the "default sword" weight. Thus, the D&D "rapier" weighs 75% of what the D&D "longsword" weighs.
That would mean that it is not the rapier of the Elizabethan era or even of years as late as roughly 1640. During that era, rapiers weighed about as much as one-handed cutting swords. The big difference was in weight distribution. For cut, more out in the blade. For thrust, less out in the blade. Therefore, to maintain the same relative weight to the D&D "longsword" we are talking about Transitional Era or later weapons. By the Transitional Era, cutting play had been relegated to backwater podunks like Scotland. Real gentlemen only pulled out the hackers for warfare.
A transitional rapier would often have a blade no longer than 36 inches. The blade would be quite thin, about as large as a "double-wide" stage blade or a practice schlaeger blade. Weight would be roughly 75% of that of a stout one-handed sword, give or take.
The epee is not a descendent of this weapon. The epee was invented in the 1800s, specifically and exclusively for duelling. It was
never meant to be worn but was always to be carried (often in matched pairs) in a case unless used. These dueling epees were even lighter than the transitional rapier, sometimes being no more than 50% of what would have been the "standard sword" of the medieval era.
In the modern day, the longest standard "epee" one can now get has a 35-inch blade. The heaviest that the FIE permits the weapon to be is about half of the average weight of the medieval standard "sword", but most modern fencers I've polled prefer to use a weight that would be 1/3 of the weight of the sword that D&D tries to represent with "longsword".
Okay, so we have a weapon that is 3/4 the mass (and it's mass that matters very often) of the "longsword" doing 1d6(18-20/X2). The epee, even one optimized for real duels, was significantly lighter than this--with a smaller wound channel due to thinner blade. So, I'd say that a good approximation would be 1d4(18-20/X2) for the "epee".