The faster your effective Speed, the faster your auto-attack animations execute, so there is less delay between the activation of your queued active skills. Since all active skills cost the same amount of power regardless of your weapon Speed, this means you will burn power at a much faster rate when using fast 1H or dual-wield weapon setups.

In short fights against single, normal "white" foes or easier, power consumption isn't much of an issue. In longer fights, however, against single "yellow" foes or harder, or against multiple foes, or against signature/elite foes, or in a location with fast respawns, you might be better served with a slow 2H weapon because your power will last longer.

The "extra swings" and +damage bonus of slower weapons are higher with slower weapons, but occur more rapidly with faster weapons

Depending on the weapon-based active skills that you tend to use most often, you might be able to generate more overall damage output by using a slower, harder-hitting weapon. In particular, this comparison applies to dual-wield setups versus 2H weapon setups:

• A dual-wield setup typically yields far more auto-attack DPS and shorter delays between the execution of your queued-up skills than comparable 2H weapons, so you have high auto-attack DPS and faster-occuring damage from your queued-up skills.
• Many weapon-based skills have a +damage bonus value that increases with slower weapons. For example skill X might do +17 damage when you are equipped with a 1H weapon of Speed 2.0 or a dual-wield setup that yields an effective Speed of 2.0, but that same skill X might do +30 damage when you are equipped with a 2H weapon of Speed 3.6.
• Many weapon-based skills effectively generate multiple "swings". For example, skill Y might deliver 3 "main hand" swings of damage, each of which also has a +damage bonus as well. The total damage output of all these multiple "swings" can be much larger with a slow 2H weapon than with a fast 1H weapon. However, there are two addtional factors to consider:
  • Many of these same skills will add in one or more "off-hand" swings when you are dual-wielding, so the gap in damage might be less than if you examine the skill tooltip with only one 1H weapon equipped.
  • A faster weapon setup might actually let you front-load more of those "extra swings" in the same amount of time as a slower 2H weapon. For example, in a dual-wield setup you might be able to generate something like 6 "extra" swings in first 15 seconds of a fight, but a 2H weapon might generate perhaps only 3 "extra" swings in that same 15 seconds. So even though each 2H "swing" is more damaging than the same "swings" in a dual-wield setup, the total of the 3 slower "swings" might be less that the total of the 6 faster "swings".

The interplay of these various factors is the main reason for stating that "you might be able to generate more overall damage output by using a slower, harder-hitting weapon". There are no hard and fast-guidelines in this regard because so much depends on the particular weapon-based skills that you use most often. Your best bet is to equip your best dual-wield setup and look at the skill tooltips, then equip your best 2H weapon and look at the skill tooltips, then do some rough calculations and tests for yourself, remembering that you'll be able to fire off your attack chains faster with the dual-wield setup.