As for the elements : some bosses (Elga) have high defense and some weakness to a certain element, which makes them more resilient to standard attacks.
With your calculations, it could be something like :
23,400 x (100 - [defense percentage])% + 3 x 600 x (100 + [weakness percentage])% for Diffusion cannon, against
22,480 x (100 - [defense percentage])% + 2 x 600 x (100 + [weakness percentage])% for Double shot.
Taking 20% defense and 15% weakness (must be around Elga's stats, feel free to correct me) : 23,600 against 22,000.
As you can see, the higher the boss' regular defense, the more efficient Diffusion cannon and elements will be. Diffusion cannon then seems to be a better choice when hitting single targets (also applies to PvP).
Now with critical rate involved : 300% critical damage, 30% final critical rate.
23,400 x (100 + 30 x 3)% x (100 - 20)% + 3 x 600 x (100 + 15)% = 43,000 (actually critical hit damage isn't calculated like this, but screw it)
22,480 x (100 + 30 x 3)% x (100 - 20)% + 2 x 600 x (100 + 15)% = 40,700
23,600 / 22,000 = 107% and 43,000 / 40,700 = 106%. It seems like higher critical rate / damage only increases Double shot's efficiency compared to Diffusion cannon as long as elements are implied ; how did you come to the opposite conclusion ?
Now as for the 'old debate', with 20,000 MATK, set critical rate and damage, no elements implied :
Diffusion cannon : 3 x (0.78 x 20,000 + 50) = 46,910
Double shot : 2 x (1.12 x 20,000 + 40) = 44,880
46,910 / 44,880 = 105%
With the 10.000 MATK from before :
23400 / 22480 = 104%
We saw that, with set critical rate and damage, elements benefit more to the Diffusion cannon, and so does an increase in MATK, given there only is one target to hit.
From this comes that Diffusion cannon deals more damage to single targets, although not by far unless you have tremendous amounts of element attack.
Edited by Homurasan, 02 August 2015 - 03:23 PM.