There are a few interesting things that Diablo 3 is doing with damage calculations, and there are a few interesting strategic choices to make based on those mechanics. I want to highlight the two that I find most interesting here.
Both will be best served by examples. I'll be using exaggerated examples here, just so you can get an idea for how the mechanic works, but the actual game will probably have items much closer to each other statistically than the numbers I'm using.
Firstly, there is a discrepancy between DPS (damage per second) and DPA (which is an acronym I just made up to mean damage per arcane power--although it also works with mana, hatred, etc.). Imagine you have two weapons: one is an axe that attacks once per second and deals 40 damage per hit; the other is a dagger that attacks four times per second and deals 10 damage per hit. Both clearly have 40 damage per second. If you were to wail on enemies with a basic attack, the only difference between the two is the frequency of damage output and the magnitude of individual hits. Overall, however, they work fairly identically.
This is also true of using skills with these weapons. Because all damage is dependent directly in item damage, and even skill attack speeds are modified based on the weapon's attack speed, you'll notice the same thing if you were using Arcane Orb, for example, rather than a basic attack. With the axe equipped, you would attack much less often but each individual orb would be much more devastating.
So far, this is all pretty straightforward. Your average damage per unit of time is unaffected by your weapon choice, so long as the DPS stat of those weapons are the same. The thing that throws a wrench in this whole equation is that the cost of Arcane Orb per cast is completely unaffected by weapon. This means that, because you are casting four times as frequently with the dagger equipped, you are using your Arcane Power four times as fast for the same DPS as if you were using the axe.
The faster the weapon, the less efficient your resource usage will be. The DPA (damage per arcane power spent) is much reduced for weapons that attack faster, if the DPS on the weapons are equal. Attacking fast is fun, and the utility of having a faster attack animation should not be overlooked. This is not to say slow weapons are the ultimate winners of the war. But if you are having trouble sustaining as a Wizard, always low on Arcane Power, consider switching to a slower weapon and see if it helps you with your resource management. This same math is true for the other classes, as well, but since the Wizard seems like it's going to be doing the most spamming and spending of resources, it is mostly likely to affect the Wizard's equipment choices more than the other classes.
The other really interesting damage-related math that will affect your equipment choices has to do with dual-wielding. The mechanics for dual-wielding in Diablo 3 are very simple: first you attack with one weapon, then the other, back and forth. Each individual attack uses only the stats for one of your equipped weapons. The DPS that is shown in your inventory is simply a calculation of the DPS you would be doing if you alternated attacks like this, averaged over a long period of time.
If you're really astute, you would be thinking that clearly, this doesn't make any sense. If this were the only thing that were done, then dual wielding would always be strictly worse than equipping one weapon. Why would you want to waste time attacking with an inferior weapon when you could be getting your damage wholly from a superior weapon?
Before I get into the solution Blizzard used to solve this problem, let's define the problem a little bit better. Again, let's say we have two weapons: a sickle that attacks once per second for 4 damage each hit, and a club that attacks three times per second for 3 damage each hit. The sickle has 4 DPS, and the club has 9 DPS. If you were to alternate attacking with these items, it would break down like this:
You deal 4 damage with your sickle
You wait 1 second
You deal 3 damage with your club
You wait 1/3 of a second
You deal 4 damage with your sickle
Blizzard realized this, and added an extra incentive to dual-wielding. If you have two weapons equipped, you get a 15% attack speed bonus. This means that weapons with DPS close enough to each other equipped at the same time give you an overall boost to your DPS instead of a penalty. If you use weapons that are still massively different in DPS, you will still suffer an overall net decrease in damage output.
These are just a few things to keep in mind in 11 days, when you're slaying the minions of hell and enjoying the new release of Diablo 3. Hopefully this little mini-guide proves helpful!