Their damage is the same at 80 - the key difference lies in AoE. For 82mm max range is 4 and near/mid/far damage range are defined as 1/2/3. For 120mm max range is 6 and damage ranges are defined as 1,5/3/4,5. Damage multiplier is 0,85/0,5/0,25. Simply put, 120mm has greater AoE and range at the cost of fire rate.
Plus, the 120mm absolutely wrecks ambient buildings.
That's for direct hits against say buildings or vehicles. The damage multiplier is set below 1 for near range so no mortar can 1 shot any model at full HP and will mostly be doing 68 dmg.
The 120mm doesn't wreck garrisons (unless it's using a different dmg type which i'm not aware of). As both do the same dmg, even at far range, the dmg to buildings is the same. Against units inside, outside of direct hits or been affected by AoE, is the same as well.
When a weapon has the property "dmg all in hold = true", they do the "far dmg" to all entities disregarding if they are in the AoE or not (remember to aim your grenades against the highest concentration window).
The only thing that the 120mm has it going for it, it's that it's easier to use due to extended range.
I've already made several test with the unit and have been saying for years that the 120mm is both overrated, overpriced and overvalue (vet wise). The unit is better now that ALL other mortars and indirect fire has been nerf (by comparison) but it's still better to get a normal 82mm if you plan to use barrage at all.
https://www.coh2.org/topic/103343/82mm-vs-120mm-mortar-against-flak-hq/page/1
Opinion: it doesn't outperform the 82mm mortar by cost (240 vs 340), popcap (6 vs 9) or vet (it has double requirements and each vet level doubles it, so when the 120mm hits vet 1 the 82mm is vet 2).