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The real winner is going to be whoever has the most and strongest psychic pokemon. Alakazam is probably the strongest non-legendary pokemon as far as general warfare goes, though pokemon like Metagross might be better in direct warfare. For defense, Gardevoir is likely the top pick, thanks to access to Light Screen, Reflect, Teleport, and Future Sight, alongside plenty of healing.
Fairy, Dark, and Ghost share some of Psychic's domains, but Psychic remains the type that's able to generate the most value during a war thanks to moves like Future SIght implying precognitive abilities, and Teleport goes from a near-useless move to the defining question of who will win the war.
Ghost-types in general would be excellent in war, with Gengar as a top-tier "Kill all the Brass" pokemon, especially because it can just pass through most barriers. But, Psychic pokemon would have the edge in intelligence gathering as well as mobility, and would also be able to act as a direct counter to many of the threats that Ghost-types pose.
Various legendaries can act as living nukes, but you don't really win wars with nukes (they are very helpful to have though). However, many do have mythical abilities that change the very dynamic of warfare, including time manipulation like Dialga or reality redefining abilities like Arceus or Jirachi. In the end, if we're going to include legendary pokemon into the mix, whoever has Victini is guaranteed to win.
