Mortars fire 36 shots (6x6) over the smallest area, which is still relatively large in infantry terms. They completely saturate their target area, so will generally hit even people in cover, and there's barely any gap between salvos.
Artillery fires 24 shots (4x6) over a medium sized area. The shots are individually more powerful than mortars but due to the greater spacing and timing, they have trouble with cover and give people ample opportunity to escape the firing zone if they're not killed in the first salvo. Artillery tends to have a 50% longer cooldown than mortars.
Rockets fire 16 shots over the same medium sized area as artillery, and they all land in a single salvo, giving no opportunity to escape. They tend to wreck destructible objects, such as cleaning out all the fences in half of a housing block in Spartanovka, but naturally provide less long-term area denial than the others and tend to have twice the cooldown of mortars.
Any of them will kill a tank on a direct hit and damage on a near miss. Due to their target saturation, mortars are the most reliable for landing that direct hit, and on Gumrak, mortars have no cooldown. Very useful.
I would agree that, right now, rockets are of fairly limited utility, but once the player base learns not to blunder their way into ongoing artillery zones, the immediate punch will be of greater value. Even now, it's useful for sweeping a cap zone clear all at once so you can move into it right away before the people killed by it get a chance to respawn.
