Weapon Damage = [Base Weapon DPS + (AP/14)] * Base Weapon Speed
Say you have 35000 attack power and a 2.6 speed weapon with 3504.4 dps (e.g. gara'kal). Your character sheet's average weapon damage will be 15611.44 (assuming MH). This weapon will have a base damage range of 6378 (0.7 * 3504.4 * 2.6) to 11845 (1.3 * 3504.4 * 2.6).
In order to match that character sheet weapon damage, a 1.6 speed weapon would need to have a base dps of 7257.15, which equates to a base damage range of 8128 to 15095 (i.e. significantly higher than the slower weapon).
In other words, any 1.6 speed weapon that falls between an average base damage of 9111.5 (slow weapon example) and 11611.5 (fast weapon example) will result in softer-hitting melee specials than the slow weapon, despite having higher base weapon damage (assuming identical stats - in reality, the faster weapon in this example would have much better stats due to the ilvl jump and would almost certainly be an upgrade). The reason for this discrepancy is weapon speed, which is directly proportional to the attack power coefficient on your special attacks, since they are not normalized (special attacks using a 1.6 speed weapon only get 61.5% as much of your AP as they would receive if you were using a 2.6 speed weapon, instead (1.6/2.6)).
And all of the above is focused purely on how hard our yellow attacks are hitting (windfury / lava lash / stormstrike / etc.). It ignores other reasons why we would want slow weapons, like maelstrom weapon's proc frequency or windfury weapon's hidden ICD. At the end of the day, speed matters much more than base weapon damage.