When it asks you if you want to skip the cutscene, it is only talking about that time. Everytime you die, it will ask you if you want to skip the cutscene.
Ultima Weapon
ATK 12, STR +9, MP +2
One Winged Angel
ATK 8, STR +5, MP -2
Ultima is definitely stronger.
Special things you should watch out for? Well, there's all the extra stuff that was added:
*2 new keyblades: One Winged Angel (defeat Sephiroth), Diamond Dust (defeat Ice Titan)
*Extra cutscenes: Riku in Hollow Bastion (after fighting Leon in Traverse Town), Riku in Darkness (after Kairi gives Sora the Oathkeeper), Sora's Memories (after defeating Ansem), and The Showdown of Fate (after defeating Sephiroth)
*New abilities: (Slap shot, Gravity Break, Ripple Drive, Stun Impact, Slide Dash, Hurricane Period, Zantetsuken, Leaf Veil, Tech Plus, Encounter Up)
*2 New Rods: Meteo Strike (chest in the Giant Crevasse in the End of the World), Fantasia (synthesize)
*2 new shields: Massive Bumper (In the Neverland section at the End of the World, in a chest), Seven Elements (synthesize)
*New boss: Unknown (Go to Castle chapel in Hollow Bastion after sealing its keyhole. There will be a portal that takes you to the fight.)
*Gummi ship missions
*All the enemies are colored differently, and have higher stats
*Proud mode (mode even harder than expert)
*New Enemies: Neoshadow (end of the world), Chimera ( (boss) Halloween Town), Pink agaricus (Deep Jungle and Atlantica...actually I think it's anywhere that there are white mushrooms), sniperwild (Traverse Town), black ballade (almost everywhere), Jet Balloon & Missle Driver (Neverland), Pot scorpion (agrabah), Stealth soldier (just a black Stealth Sneak), Grand Ghost (Giant search ghost), Giant Shadow
*Deep Dive
*3 New Ansem Reports (defeat Kurt Ziza, Sephiroth, and the Unknown)
*Goofy has 1 new ability: Evolution (Donald has no new abilities)