Im not sure where you got this from, but this is simply wrong.
Base 1-h damage on this sword is 13-30. Base exe 1h damage is 24-40. Average damage is 21.5 VS 32... - literally 50% higher for exe. So yeah.. - exe base is FAR superior in terms of damage...
1H damage on this sword is 38-101. Exe would only need 115% ED (without +min/max) to achieve the same damage... Sure, the reqs are low, but there is no universe in which a barb using this sword 1-handed and having 91 str can kill ANYTHING in hell. So yes, it is indeed charsi.
dude, i've played an exec barb where i used it 1-handed sometimes as well as many other 1-handed swords for fun.
His exec with 148% ED and +10 Max has 109 max damage 1-handed and I killed shit just fine with him.
(So your numbers are simply wrong)
It's a little thing called crushing blow either way.
The Dacian Falx has very low 2-handed damage, but with extremely high ed and max dmg rolls, it rivals the 1-hand damage of a mid-rolled exec.
For a fraction of the stat reqs.
TO BE MORE SPECIFIC FOR YOU.