What does more damage overall, dual wielding or two handed weapons, assuming full specialisation on both? Has someone crunched the numbers yet?
Depends on the build and weapons of course. Let's due ranger since it has spec for both without going for a dex build. Here's an example of apparently similar damage. 18 STR (for easy calculations). No sources of damage bonuses other than STR. Assume the ideal case that you always hit. If not, we can just simply multiply the average damage number by the hit chance to see our conditional average damage. Miss chance is just a chance for 0 damage. For this same reason, we can assume that if a crit happens, you'll automatically confirm. This makes the calculation a lot easier though we can simply add some multiplicative factors if you want to factor in hit chance into the average damage. I will use greatsword and two shortswords as the example since without bonuses it's 2d6 damage for each and the same crit chance. We'll focus on averages here. Standard deviations can be done later if one wishes.
Let's start with no bonuses. Average damage for Greatsword
(0.9)*7+ (0.1)*14 = 7.7 damage
for short sword pair
(0.9)^2*7 + 2*(0.9)*(0.1)*10.5 + (0.1)^2*14 = 7.7 damage
They're the same damage on average and predictably the same standard deviation. So we'll add in bonuses as we go along and see what happens
Greatsword
2d6 + 6 at 19-20 x2
8 - 18 damage each attack with 16-36 damage on crit for each attack. Average damage on each hit should be
(0.9)*13 + (0.1)*26 = 14.3 damage
Two shortswords
1d6 + 4 at 19-20x2 (main hand)
1d6 at 19-20x2 (off hand)
Each pair of attacks is 6-16 damage. Crit on at least one strike is either 11 - 26 (only main hand crits), 7 - 22 (only off-hand crits), 12-32 (both crit). Average damage for each pair of hits should be
(0.9)^2*11 + (0.9)*(0.1)*18.5 + (0.9)*(0.1)*14.5 + (0.1)^2*22 = 12.1 damage
So Greatsword hear does more damage.
If you take double slice with the shortswords build. Now both weapons are at 1d6+4 damage. So no crits is 10-20 damage, only one hand crit is 15-30, both weapons crit is 20-40 damage. This gives an average damage
(0.9)^2*15 + 2*(0.9)*(0.1)*22.5 + (0.1)^2*30 = 16.5 damage. So here the shortswords build does more damage assuming you always hit.
Now lets factor in Power attack. With level 1 power attack Greatsword damage is 2d6+9 and we have two shortsword attacks at 1d6+6. As before, we can predict that dual wielding here will do more damage. Similar calculations as before the average damage for greatsword is
(0.9)*16 + (0.1) * 32 = 17.6
(0.9)^2*19 + 2*(0.1)*(0.2)*28.5 + (0.1)^2*36 = 20.88
So more damage in general if you can't miss.
Now if we assume that our hit bonuses are exactly enough to get a 95% hit chance. For example the enemy has 20 AC and you have a modifier of exactly +18 so everything but a 1 is a hit. Now we have to apply a modifier for the second attack for the dual wielding build and we have to redo the calculations to account for this with all bonuses. For the Greatsword,
(0.95)*(0.9)*16 + (0.1)*(0.95)*32 = 17.6*(0.95) = 16.72
The computation for the offhand now changes and becomes more complicated. The main hand is at 95% chance to hit. But the offhand is at 85% chance to hit. So we can add these two factors into the mix. We'll write down the factor for every combination since now the offhand or main hand can miss so we add in the chances of that happening to our average
(0.95)*(0.15)*(0.9)*9.5 + (0.95)*(0.15)*0.1*19 + (0.05)*(0.85)*(0.9)*9.5 + (0.05)*(0.85)*(0.1)*19 + (0.95)*(0.85) * 20.88 = 18.79385'
Let's lower the hit chance to 50%. The greatsword average damage is
17.6*(0.5) = 9.8
The shortsword does
(0.5)*(0.6)*[(0.9)*9.5 + (0.1)*19] + (0.5)*(0.4)*[(0.9)*9.5 + (0.1)*19] + (0.5)*(0.4)*20.88 = 9.401
So the lower your hit chance, your average damage is higher with the greatsword. If you have a higher hit chance in general, you'll do more damage dual wielding.