HVG - Vergil w/ DT'd Starfall JCs and Summoned Sword spamming (anytime I say Summoned Sword spamming, it's referring to simply spamming swords instead of using the various formations)
Cerberus - Vergil. Dante has more options to deal with Cerberus' icicle drop spam (especially when Cerberus upgrades himself to "red" phase). Still prefer Vergil with Aerial Rave and Summoned Sword spam.
Gigapede - Dante. All Vergil really has is Judgement Cut lvl2 and maybe reflecting a few orbs (though dangerous) with Aerial Rave or Lunar Phase.
Jester - Vergil. On Very Hard/DMD, having Air Trick and Summoned Swords is a godsend for wearing him out. For the later fights, Aerial Rave/Summoned Sword spam.
Agni & Rudra - Either. Dante is fun with easy Royal Guard Just Release+DTE, while Vergil has Summoned Sword spamming to stagger the brothers without necessarily needing to parry to stun them.
Leviathan Heart - Dante. He has the superior damage options.
Nevan - Vergil, for Judgement Cut lvl2 for cutting down her shield, and then DT'd Beowulf Combo+Summoned Sword spam
Beowulf - Vergil with Aerial Rave spam, along with Yamato having a elemental advantage against Beowulf. Dante does have more damaging options against Beowulf, though.
Geryon - Dante, just because the loop is easier with him.
Lady - Vergil for playing catch-up and at least being able to squeeze in damage w/ Swords during her second phase.
Doppleganger - This battle is mostly just reflecting Doppelganger's Zodiac, so either is fine.
Arkham - Vergil, especially once phase 2 kicks in. Vergil can still use Judgment Cut lvl2 and swords for some good damage.
Vergil/Vante - The fights are fun with either one. Vergil partially has the advantage since Sword Storm is an easy way to get rid of Spiral Swords, also JC'd lvl2 Starfalls.
"I think it's time to switch condiments, 'cuz that weaksauce ain't helping!"
I'm playing through DMC 3 HD and Geryon's on my nerves. I got through Beowulf (Pazuzu) just fine. Cerberus gave me s*** for the longest time, still sorta does, but so far Geryon pisses me off to no end.