Nader beats Demoman (grenade launcher + reliable damage)
Fletcher beats Demoman (not so sure about this one actually)
Scout destroys Proxy (huge speed advantage + double jump over mines)
Aura beats Medic (more reliable damage and better self heal)
Phoenix beats Medic (more reliable damage and better self heal)
Sawbonez beats Medic (more reliable damage and better self heal)
Sparks beats Medic (range advantage, more reliable damage, and better self heal)
Lucio beats Aura (sonic blast takes aura off of health station, removing her heal, dealing damage, and taking her shotgun out of range, Lucio can keep himself alive and keep aura out of effective range for a long fight, chipping away at her health)
Pheonix beats Lucio (more reliable damage, better self heal)
Sawbonez beats Lucio (more reliable damage, better self heal)
Sparks beats Lucio (range advantage, more reliable damage, better self heal)
Vassili beats Widowmaker (Vassili has more reliable spotting, quicker damage output [Widowmaker must charge shots], Widowmaker’s venom mine isn’t effective enough, her hook won’t give a great enough advantage)
Vassili beats Sniper (Vassili has a spotting ability, way quicker damage output)
Vassili beats Ana (sleep dart is harder to hit at longer ranges, Vassili has a spotting ability and better overall damage, healing grenades won’t heal a headshot [cause you’re dead])
Aimee vs Widowmaker: defender wins (Aimee has far less utility on offense, but great ability on defense, as does Widowmaker)
Aimee beats Sniper (quicker damage output, spotting ability)
Aimee beats Ana (better overall damage, spotting ability, low sleep dart utility, healing grenade won’t heal dead)
Engineer obliterates Bushwhacker IF the engineer gets his turret up. Otherwise, Bushwhacker wins because of better weapons, and the Engineer’s lack of ability to take out a Bushwhacker turret (have fun killing a turret with a shotgun)
Spy beats Phantom (Phantom’s cloak is NOTHING in comparison to the Spy’s, and if backstab is included, which I am, Phantom quite literally won’t see it coming)
Heavy beats Rhino (range advantage, not entirely sure about damage difference though)
The last three I cannot judge
TLDR; Dirty Bomb mercenaries win most engagements due to a focus on guns, which are much more reliable than projectile weapons, though a select few have kits that perform especially well against some of the dirty bomb kits