It actually can have more dps than the Terra Blade.
It can not unless you reach one swing speed modifier so high it will be so obvious you are cheating the values in even the game will flip off and tell you.
Under normal values, both weapons DPSs are:
Terra Blade: (frameRate / useAnimation) * (damage + (damage * 25% projectile damage)) = (60 / 16) * (88 + (88 * 1,25)) =
742,5
Horseman's Blade: (frameRate / useAnimation) * (damage + (damage * 50% projectile damage)) = (60 / 26) * (75 + (75 * 1,5)) = 432.7
Only one pierce of Terra Blade's projectile i took into consideration, as it's the hit that will most likely hit during the swing, considering Horseman's Blade can only deal full DPS on close quarters. If the extra two pierces of the beam are taken into consideration, Terra Blade's DPS would be
1567.5. At long range, the beam would be able to deal a minimum DPS of 412.5 (single target) and a maximum DPS of 1237.5, Horseman's Blade has no long range capabilities, aka its DPS is 0 in this case.
Damage modifiers increase the DPS difference even more, but melee speed modifiers do improve Horseman's Blade dps as extra swinging speed does not improve Terra Blade's beam fire rate but it does increase the speed at which the pumpkins from the Horseman's Blade are spawned, but even if we take an huge melee speed modifier (lets say 100% extra melee speed), the DPSs would be:
Horseman's Blade: (60 / (26 / 2)) * (75 + (75 * 1,5)) = 865,38
Terra Blade: ((60 / (16 / 2)) * 88) + ((60 / 16) * (88 * 1,25)) = 1072,5
Guess what's still superior.
NOTE: THIS APPLIES TO PC. I do not know if console already has the Terra Blade buff which happened post Frost Moon update. Any claim of Horseman's Blade being slightly better than Terra Blade prior to said buff are partially right, as while Terra Blade still had more base DPS, melee speed did let Horseman's Blade reach enough to surpass and a much higher DPS because of Terra Blade's beam mechanic not being affected by such stat.