Seymour Omnis has access to all of his skills displayed in FFX, though he does not have the Mortiphasms with him.
Leon Kennedy is as seen in Resident Evil 4. He has access to his Semi-Auto Rifle, Matilda, Infinite Launcher, Striker, 5 Incendiary Grenades, and 5 Flash Grenades, and they're all fully upgraded with all their respective attachments.
Luca Blight is as he appears in his boss fight(s). He has access to all of his attacks, but not the Beast Rune, which he never used because the damn thing was sitting in his castle.
Ryu Hayabusa is as he appears in Ninja Gaiden 2, with all his weapons fully upgraded, as well as the Enma Fang and Howling Cannon from 2 Sigma.
Sephiroth is as he appears in Final Fantasy 7 and the Kingdom Hearts series (minus his Heartless Angel technique), with his legendary sword Masamune, limited teleportation, and access to his FFVII PC form magic. He may not use his Bizarro or Safer forms (or their magic), and no, he doesn't have Supernova.