A quick rundown of various explosive weapons, starting at the more common and/or lower tier cannons:
A quick aside, but I will assume that all cannons are shooting HE instead of Piercing. You bring them for the boom, not the dakka, so they will be judged accordingly.
Assault Cannon: D-tier with Cannonballs, C-tier with other ammo. It's slow to shoot and slow to reload, so you'll usually only get one shot every other round. Pretty bad with the round shot cannonballs, but pretty decent with the explosive, incendiary, and chemical cannonballs. Cannon HE is the same 60 damage as a 40mm Grenade Launcher, but much heavier, less accurate, and slower to reload. Accuracy scales off bravery. Better used as armament for a Gunwagon.
Mini Cannon: D-tier, similar to Assault Cannon but smaller and worse. Similar mobility to the grenade launcher, but worse damage.
Spitfire: C-tier, a fun little shoota that sprays small explosions everywhere. More of an autogun that explodes than a real launcher. Typically seen in the hands of Spartan Heavys. Ammo belts can be worn on the head for true rambo style. Suffers from mediocre damage and struggles to penetrate mid-tier armors.
Light Cannon: B-tier, an average and reliable antipersonnel explosion projector. Can reliably chunk Osiron Security and other mid-tier armored goons. Slightly less damage than a grenade launcher.
LACC: C-tier, often seen in the hands of Osiron Security. It's like a Light Cannon mixed with a rifle, or a superheavy rifle with optional explosive shots. Special mention to WP ammo, good for lighting werewolves and ninjas on fire. Beaten by LC and other larger exploders, while the heavy automatics have better mid-tier kinetic shooting. That said, I respect its power to punch through Tac Armor and it has killed many gals.
Autocannon: Unrated, haven't used the oldxcom AC
Man-Portable Autocannon: C-tier, effective fire support but lacks mobility and punch. Can pretty much always put 3x autocannon shots downrange and the arcing fire helps it do so out of LoS. Park it on your flagship's roof and use it to demolish houses. Becomes B-tier when being used to deliver special ammo types: AC-GAS ammo excels against Deep Ones and Lobstermen (or unprotected humans), and rare AC-CRY ammo lights zombies, 'lids and vamps on fire.
Grenade Launcher: A-tier, genuinely one of my favorite guns. Never leave home without a grenade launcher (or two!) in your squad, and sprinkle your explosions around liberally. Park your grenadiers on elevated terrain, kneel for extra accuracy, and enjoy your budget artillery. The more exotic ammo types (shoutout to Black Napalm and 40mm Gas) help it stay relevant throughout the midgame, and later upgrades into Smart Grenade Launcher and 40mm Hellerium, Fusion, and EMP help keep it relevant even further beyond. It's single shot so you get to experience the tactile joy of reloading every shot, but the ammo is 1x1 so you can bring as much as you can carry.
Assault Grenade Launcher: B-tier, sidegrade to Grenade Launcher. Same damage, 8 round clips, better for frontline assaulting rather than fire support.
T-T Grenade Launcher: B-tier, upgrade to Grenade Launcher's indirect fire support role. More damage and more accuracy but without the exotic payloads. Would be A-tier if it had gas, EMP, and fusion shells.
Blizzard Pocket MLRS: C-tier, same punch as a Grenade Launcher in a meme-y package. Will yeet six rockets downrange and create some terrain gaps and smoke clouds for you to exploit, but struggles as an anti-personnel weapon.
RPG: A-tier, the other one of my favorite launchers. Never leave home without an RPG (or two!) in your squad. RPG /DP is an all-purpose problem solver that can be relied on to remove just about any battlescape trouble spot. I like to think of it as my "Bypass Encounter" tool. Its biggest advantage is the 1x2 ammo which can fit in the quickdraw slot and the belt slots; this allows it to reliably reload-and-snapshot or reposition-and-snapshot in most situations, so the RPG is very responsive for quickly putting a rocket on target. Upgrades to Advanced RPG.
Quad Launcher: B-tier, as seen in Commando. Slightly less damage than RPG and shares the same "reloads carried on belt" utility. Can pack 8 rockets while doing so instead of 3+1, but lacks the spicer ammunition to retain utility as the game progresses.
UAC Rocket Launcher: C-tier, mostly a mook weapon for doomguys. Similar 'portable light rocket launcher' niche as the RPG and Quad, but worse damage; only slightly better than the 40mm grenade launcher. Still worth using if it's your only rocket launcher.
Recoilless Rifle: B-tier, the complimentary weapon to RPG's "solves almost every problem". The R-Rifle does not produce any explosions which is why I put it in B-tier. Instead, the R-Rifle is a specialist weapon - This thing is your poor gal's lascannon. The basic R-Rifle shells deal slightly more damage than a Heavy Gauss with 40% armor penetration on top of that. If it's too heavy for the RPG to crack, get the R-Rifle. If it is at all vulnerable to piercing damage the R-Rifle will kill it. This thing is also the reason why you can safely discount the kinetic ammo on the mid-calibre cannons like LC and AC; in any situation where you would prefer a kinetic to an explosive you can skip straight to the R-Rifle.
Rocket Launcher: B-tier, the RPG's big sister. Suffers from larger ammo that must be carried on the back, so it's slower to reload and a bit more awkward to deploy. Generally able to fire every other turn in a shoot, reload & reposition, shoot cycle. Very killy, but not as mobile and responsive as the RPG. Becomes A-tier with upgraded ammo such as Anti-Tank Rocket, MAG, Gas, EMP, etc. When you absolutely need to remove a cluster of Deep Ones, Gas Rocket. When you absolutely need to remove a merc hovertank, crack the shield then use an AT Rocket.
Panzerfaust: A-tier, panzerfaust my beloved. Single shot, 20kg, fits into any empty back slot just like a sword. Same damage as the Rocket Launcher's ordinary ammo with 10% better armor penetration. A single shot rocket launcher that can be added to any gal loadout that can carry it. Arcing trajectory, so a miss usually hits somewhere nearbv. Sprinkle a few into your loadouts, they'll come in handy.
LASS: B-tier, as the Panzerfaust but RPG-sized instead of Rocket sized. A panzerfaust for your peasants and slave soldiers; give him two, point him towards the enemy and tell him not to come back.
Mortar: B-tier. Shares many of the rocket launchers mobility and reload problems, and so can usually only fire every other round. What a shot though. Damage is midway between RPG and Rocket, but has a large area effect and can reach the entire map. There are very few times when I feel justified grabbing the mortar (because other explosive projectors usually get it done quicker), but the few times you grab the mortar you will enjoy the show. Mortar Acid shells are excellent anti-structure munitions, while Mortar Gas will remove any unprotected biologicals (and especially deep ones) with extreme prejudice. Upgrades into Servo Mortar.
Hand Mortar: A-tier, for gals only. What if you didn't have to "set up" the mortar? What if, after emptying it, you could bludgeon somebody with it? It's so lovingly orky.