In each group (swords 1h, swords 2h, axes, fencing 1h, fencing 2h, maces 1h, maces 2h) as you look at each weapon going from fastest to slowest the base damage (for the most part) goes the other way. So the fast weapons have low damage and the slow weapons have high damage.
This means that in each group there is an average. Though this average is dependant on what swing speed you can reach. There are also a few weapons that don't follow the average.
The base damage of the weapons that can reach the swing cap depends on what stamina and SSI you consider the average.
If you consider 150 stamina, 30 SSI something easily reachable then 3s weapons offer the highest base damage.
The 3s weapons in each class have the following base damages:
Swords 1h, 13-15
Swords 2h, 15-17
Axes, 14-16
Fencing 1h, has no 3s weapon but at 2.75 is 13-15
Fencing 2h, 14-16
Macing 1h, 14-17
Macing 2h, has no 3s weapon but at 2.75 is 13-16
So if you compare the 1h weapons they're pretty much the same, Fencing gets the same damage as Swords but one tick faster (which means 30 less stamina for you). Macing is better than both.
Macing 2h is 1 damage less than Swords 2h but reaches it 1 tick faster (again you'd need 30 less stamina to get that)
Ornate Axes, Diamond Maces & Black Staffs are the exception to the average in each class.
Then if you take into account special moves the only really worthwile special moves in PvM are Whirlwind & Feint. Whirlwind is available on Radiant Scimitars, Halberds, Kami, Black Staff, War Hammer. Feint is available on Bokutos, Daisho, Leafblade, Tessen, Nunchaku. Of those, the ones that are closest to the average for speed and damage are Black Staffs, Radiant Scimitars & Leafblades.
However Black Staffs can't be crafted so good ones are hard to find.
Leafblades can be crafted with UBWS.
All in all its best to go with Macing or Fencing, personally I go with Macing for its higher damage and Whirlwind I use UBWS Leafblades if I need Feint. This is also because I have good Black Staffs & Diamond Maces, if I didn't I'd probably go with Fencing.
I don't know why people get the impression Swords are superior when they aren't.