Need to take a minute to pull all the votes out, but for QUEEN vs. Solofia...
If you allow EXAs, Queen should maul - 74% average speed for Solofia (granted, turn-based, respect, blah). Queen can equip for a bit more speed with her Mach Fist, that should allow her to EXA often enough to just flat out kill.
If you add Alena's critical rate into an average damage for DQ4o, Solofia does not heal-lock with a physical (damage average rises to 138, physical + Lightning is 2.26, Queen is 98% durability before Rakukaja).
If you don't allow EXAs and don't take criticals into average damage, then this is a fight. Solofia barely heal-locks (1.72x damage from Lightning + 0.84x physical). Queen's evasion isn't supreme unless she's maxing for it (Judge of the Dead + Mach Fist + Maillot = 40% evasion or so), although that probably wins her the fight with the dodges. Queen has 57% brainwash from one of her guns and 20% dizzy from anoth....
Mmm...20% dizzy on the gun is a 74% chance to inflict. Nuclear damage gets a technical from that. And it lasts 2 turns, meaning Solofia will likely miss physicals. Solofia is only 105% HP. Technical'd Atomic Flare is 579 x2 + gun attack of ~160 = 1318 vs. a physical average of 330 = 3.99x damage. So...Queen can kill. So then we get to the situation where Queen can run Solofia out of MP. Go first, inflict dizzy. Solofia can try to physical, and miss. Queen then uses Freidyne (510 damage technical'd, 1.5x average damage) to force Solofia to heal. Could run her out of MP then. Of course, Fendspell...wrecks that. Zenethian Sword casts dispel IIRC (so if you don't allow item-casts, that's something), so no costs there. Solofia...probably has the advantage overall. Solofia just has to cast that Fendspell, and there's not much that can be done otherwise. Vajra ailments are her best bet here. Or that gun that inflicts a random ailment. If you see her being heal-locked, she loses, probably.