For instant death, be it conferred by a special rule or acquired by doubling the opponent's toughness, you get all applicable armor, cover, or invulnerable saves. Of course you still apply the AP of the weapon you are using. You cannot take feel no pain against ID, and reanimation protocols are reduced by 1. So a 5+ reanimation would be a 6+ against an ID wound.
Really terrible videos about tiny plastic space elfs intended to help you get gud scrub:
Flawless pieces of literary perfection: