Anyway... it's a given that Western Martial Arts/Historical European Martial Arts/Baritsu would be more Dante's thing (please, let's have him do a Sherlock "slo-mo-mind-reading-fight-scene" with Vergil), but I honestly think that Vergil would only use Martial Arts from Korea (Tae Kwon Do and Hwa Rang Do) and Japan (Koryu Bujutsu and Iaijutsu -- Samurai Martial Arts).
Seeing as how he more or less takes his philosophy (at least on a superficial anyway) from the "Nationalistic Pride of Japan" (which means "Yamato," more-or-less) he most likely wouldn't associate himself with any martial arts from China.
So why Korea? Because his katana-spinning and tornado kicks are very much inspired by that region... besides, a lot of Koreans who were born in Japan (they're no considered Japanese citizens because their parents are Korean) are in the Yakuza...
... Ergo, Vergil has an "appreciation" of both the dark and the traditional sides of Japan, defining him as a person of contrasts... much like Sparda, only more subtle.
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As you can imagine, Japanese-born Koreans are more or less ostracized by "traditional Japanese society" (the older, more xenophobic generation) -- thus, they have no choice but to turn to a criminal life (like the Yakuza) in order to just put food on the table (let alone live a comfortable life).
