I've been thinking about the effectiveness of cannons vs mortars in the first few minutes. If the wiki is right, then:
Cannon: 12 dmg / 0.25 energy = 48 dmg per energy, and rate of 12 * 3.75 = 45 dmg per second
Mortar: 161 dmg / 3 energy = 53.7 dmg per energy, and rate of 161 * .33 = 53.1 dmg per second
But for a mortar to achieve that, it needs to fire into creeper ~3 deep, and no less, which is only achievable continuously with a lot of pausing micro, or with a very strong source of creeper nearby (very close to emitter or when firing into digitalis). In my experience, often a continuously firing mortar will only be hitting creeper between 1 and 2 deep, which is quite inefficient energy-wise compared to a cannon.
Another issue with mortars is that they depress creeper much farther away, which results in significantly greater creeper flow from [outside mortar range] to [inside mortar range], which results in more creeper you'll have to kill that you wouldn't have to deal with otherwise. This is especially apparent when firing into digitalis.
Cannons need line of sight and proper elevation, but from most starting positions that's not a problem.
Mortars do deal slightly higher damage per unit, which can be useful later on when energy efficiency isn't an issue and when there are limited 3x3 squares within range of the creeper front to place units.
But it seems to me that in the beginning, cannons have an overwhelming advantage over mortars in the vast majority of situations when you're just trying to build up energy income and want to be as efficient as possible with your energy expenses. I can only think of a small handful of maps I've played where early creeper flow was so strong that I would have been able to continuously fire into 3-deep creeper with a mortar without wasteful overdamage.
I used to habitually build mortars whenever I saw approaching creeper that was deep, but it looks like that was a mistake. Does this sound right?
Recall that the Mortar has greater range, that it is more expensive to build, and that your objective is not maximal destruction, but minimal outflow. Creeper is conserved (for practical purposes) during flow. Also, a void behind will drain Creeper from the front, which is where you want to keep it away from.
The short answer seems to be that it is heavily situation-dependent. For maximised damage:energy, you want a PZ Bertha firing into the kind of depth that is contained only by Void and distance.
There is also the question of whether Terp + Mortar outdoes the competition. &c. &c. &c.
With elevation, well-placed Mortars generally have at least 1 terrain height advantage in the early game, generally 2+.
As with many things, a combination is probably best. Mortars for Creeper thinning, PCs for keeping the film that remains away from anything important.
My typical rule of thumb is to only use mortars extremely early when the creeper comes in thick enough to overwhelm cannons before I can get a good energy supply going. In these situations, it sometimes helps to micromanage the mortars to slow their rate of fire to keep the energy consumption manageable.
Energy is life.
'Max damage per shot' on its own isn't entirely helpful in most cases, especially for the PC, but the general flavor of the analysis is that it's much easier to get high efficiency from mortars than PCs because the former automatically target to deal maximum damage rather than targeting the nearest creeper, which is often quite thin in many practical situations. More accurate would be to say a PC shot does 1+11cells*1 which is to say that the targeted area has to be close to or exceeding one elevation level for PCs to get near-optimal efficiency. The only major time this is possible is when firing off of a ledge and into deep creeper. That being said, under continuous fire the targeted cells generally don't stay deep for long, making this technique almost exclusively a defensive tool.
(I didn't now test the workings of mortar damage in CW3, nor do I have much interest in so doing. Even my testing now was more to make sure that the targeted cells behaved more like CW1 where n cells are targeted than like CW2 where the targeted subcells are exactly those in a fixed shape about the hit subcell.)
Anecdotally, a mortar can knock down creeper and keep it from climbing over almost it's entire range, and can reduce creeper strength on flat land to almost keep it from even advancing. Cannons don't, they get overwhelmed easily.
PC's are better at holding a certain elevation especially to obtain more land for another collector, or to stop creeper advancement on flat land.
Cannons seem the go to in very early on stages. However a mix of both is always crucial for maximum effectiveness i find.