General rule of thumb is that Classes with Instant special attacks using weapons prefer the higher damage and hence slower weapons, while if you rely on constant hits to appl y eg Threat you prefer faster ones.
Note that Scopes and Sharpening Stones etc (flat damage buffs) relatively benefit faster weapons more, as you deal more often White damage and that is the damage those flat buffs increase.
Most importantly though is keeping an eye on actual damage range, especially if your Class relies on White damage much.
For example, with my Paladin I for a long time only had Crafted weapons and the damage of the Uncommon Heavy Mace (crft 20) and Uncommon Heavy Copper Longsword (Crft 14) is roughly the same - though the first allows for a Shield, saving the Healer’s manapool.
So even when DPS’ing going ‘sword and board’ was the way to go, also because it made off-tanking etc. simpler and my survival soloing better. Once I got an actual Blue weapon (Cruel Barb yay) there was no contest, at all - even though some people thought it looked ‘weird’ and was ‘wrong’ (same with wearing an Azure Hood - basically first headpiece for non-Engineers, Armor is Armor, and there is no room for ‘Gear Type Fashionista’s’ in Vanilla Gearing esp for Paladins, as healer you WILL wear a dress eventually)