Well, in real life, there's really not that much difference in speed between them. See here:
There are several things to note here:
First and most important, these guys are fighting under the assumption that neither is wearing armor. This is because modern medieval fencing is based on old fencing manuals which were mostly about unarmored fighting, as was common in duels and of course street brawls. This is the only reason the longsword guy acknowledges most of the rapier guy's hits. All the protective gear is just for safety---they're using steel training swords that are easily capable of breaking bones even though dull. If longsword guy was in armor, none of the rapier cuts and few of the thrusts would have done anything, and none hit hard enough to rattle his brains.
Second, this is a longsword, not a greatsword like the Exanima 2-hander. But as you can see, there is little difference in speed, and not much more with a greatsword.
Third, note that the rapier guy stands sideways and does most of his actions with his wrist and elbow. That's where the 1-hander's speed comes from.
Finally, note that most of rapier guy's attacks are thrusts, which are WAY faster than swings. When that becomes available in Exanima, then perhaps your perception of 1-h vs. 2-h will change. Although note that longsword guy started using a lot more thrusts himself towards the end, and they were fast enough that rapier guy couldn't stop them.
