Are the attack speeds of weapons offset by their damage output?

Here's a small exmaple of how DPS works in Skyrim. The DPS if smithed row shows how DPS will change if all weapons get the same smithing bonus damage of 46 (smithing gives a flat increase to damage instead of scaling to base damage)

Weapon              Damage  Speed   DPS     DPS if smithed
Deadric sword       14      1       14      60
Deadric greatsword  24      0.7     16.8    49
Deadric warhammer   27      0.6     16.2    43.8
Deadric battleaxe   25      0.7     17.5    49.7
Deadric dagger      11      1.3     14.3    74.1

As you can see, the weapons are more or less balanced without smithing, but with smithing speed wins over base damage every time. I'd recommend one-handed weapons unless you're not interested in smithing or not obsessed with having the biggest numbers.

Here's some numbers with +12 weapon damage (requires ~130 smithing skill and the smithing perk).

Weapon              Damage Speed   DPS   DPS@+12damage OnePowerAttack@+12
Deadric sword       14     1       14    26            52
Deadric greatsword  24     0.7     16.8  25.2          72
Deadric warhammer   27     0.6     16.2  23.4          78
Deadric battle axe  25     0.7     17.5  25.9          74
Deadric dagger      11     1.3     14.3  29.9          46

If you just want to stand there slashing (and if reach isn't an issue), dagger wins. Dagger is also good for rapidly applying weapon enchantments. And it is the sneak attack weapon of choice.

If you want to do a double critical charge attack, then you should use a two hander.