Dream of the Shore Bordering Another World (Chrono Cross) vs. Battlefield of Steel (Princess Waltz) - SPLAT.
Cradle of the Ivory Moon (Soul Nomad and the World Eaters) vs. Nightless City Guara Bobelo (Wild ARMs 4) - Close. Both competent songs that still don't really strike my fancy.
Idola the Fanatic Viper (Phantasy Star Online Episode 4) vs. Theme of Arcueid (Melty Blood Act Cadenza) - Fanatic Viper's individual sections sound cool, but doesn't really form a cohesive whole to me.
Bridge of Jade (May Sky) vs. Bombing Mission (Final Fantasy VII) - The Bridge explodes.
Main Theme of Final Fantasy VII (Final Fantasy VII) vs. Wanted Person Battle (Metal Saga) - Admittedly biased by the magnificent orchestration of the main theme, but even the in-game version is really awesome. And probably would have beaten Influence of Truth's Appearance to me, too.
Antipyretic (Final Fantasy Tactics) vs. EXEC_PAJA/.#Misya Extracting (Ar Tonelico) - Not close.
Waste Abandonment Pit (Breath of Fire V) vs. There's Only One Family Named Schroedinger (Wild ARMs 3) - More active? I like subtle background music, but this might be too subtle.
Sorrow's Distortion (Castlevania: Order of Eclessia) vs. Song of Mana (Legend of Mana) - I think my favorite song from Ecclesia is the undersea music, of all things ("Wandering the Crystal Blue.").
FAILURE BRACKET
Waterfall (Koudelka) vs. Dragon Slayer (Dragon Slayer) - Waterfall still authentically good.
ANIME
Shangri-La (Sakyuu no Fafnir) vs. Salva Nos (Noir)
Senketsu no Chikai (Magical Pokan) vs. Rinbu Revolution (Revolutionary Girl Utena) - Senketsu no Chikai doesn't do it for me.