Test platform: Sunder with no skills, 20 capacitors, 20 vents, ITU, stabilized shields, extended shields, hardened shields, choice of one large energy weapon.
Test 1: vs 1x balanced Hammerhead
Test 2: vs 1x close support Lasher, 1x standard Lasher
Test 3: same as test 1, but I put the Sunder under AI control.
I don't see any need to test versus the Lashers with AI control on the Sunder - the Lashers should beat that every time.
Test results:
Spoiler
ORA Invocation Launcher:
Test 1: Sunder wins, at no risk, though it costs the sunder nearly 200s of PPT.
Test 2: the Lashers win.
Test 3: Hammerhead wins, after the Invocation Launcher breaks due to low CR.
Adloquium Plasma Railcannon:
Test 1: Sunder wins, at no risk, and only 50 seconds of PPT.
Test 2: Sunder wins, at cost of ~30s PPT. Moderate risk - while you're killing the first Lasher, the second one will push you pretty high on flux.
Test 3: Sunder wins, at no risk, costs ~180s PPT.
Purgatory Shock Cannon:
Test 1: Sunder wins, still at no risk, and still costing about 50s PPT.
Test 2: Sunder wins, at cost of ~30s PPT. Risk about the same as with the Adloquium.
Test 3: Sunder wins, at cost of ~280s PPT - it doesn't get the kill until it pins the Hammerhead against the map edge, but it's never at any risk of taking damage.
Plasma Cannon:
Test 1: Sunder still wins, but requires some care in piloting as it can't just outrange the Hammerhead; cost me about 40s PPT, and was able to avoid taking more than trivial armor damage.
Test 2: Sunder wins, at cost of ~20s PPT. Moderate risk, though no damage taken.
Test 3: Sunder wins, but down to about half hull and 44% CR.
Autopulse Laser:
Test 1: Still a tricky fight; was able to win without taking damage past shield, but it was close. ~50s PPT used.
Test 2: Basically identical to the plasma cannon test, though I got a lot closer to taking damage on this one. ~20s PPT used.
Test 3: Sunder wins, takes ~500 damage from a harpoon it didn't bother to shield, and costs ~100s PPT.
Now, is this a fair test? No, of course not. But it's still a useful one.
There are clear outliers here: against the Hammerhead, all three of the mod weapons I tested allow for victory with zero risk - the Sunder doesn't even have to put its shields up if you fly it right. However, of those three, it's only Sylphon's guns that offer a reasonable kill time, neither far behind the much riskier fights with shorter-range vanilla weaponry.
Against the Lashers, by contrast, there's no option for a no-risk approach to the fight; whichever Lasher you focus on (it had better be the close support variant), the other will close in and attack. For these fights, the vanilla weapons are understandably better: both offer better chances at killing one Lasher before it can get out of range and reset - the plasma cannon from raw DPS, the Autopulse from burst damage.
* * * * *
Based on this, though, I do have to revise my statement on why I consider the Invocation Launcher closer to vanilla balance than the Adloquium or the Purgatory. It turns out it's not the shot speed that's the primary factor, it's the combination of a very low firing rate (so targets can lower shields inbetween shots) and extremely low armor penetration (so that it takes a large number of hits past shields to destroy even a frigate.)