I know you only wanted an answer for Erika, but I included extra info because both Pokémon are useful for most of the game.
You should use Alolan Vulpix. It may not resist Erika's STAB, but it hits hard with Ice Beam. Ice/Fairy is generally a better attacking combo in LGPE than Fire is, being particularly strong against Giovanni and the Indigo Plateau. With 109 base Speed, Alolan Ninetales is also faster than many opponents, which lets it clean up matches more efficiently.
Alolan Ninetales' 4x Steel weakness is problematic at first glance, but the only Steel type Pokémon in the game are Magnemite, Magneton, Meltan, and Melmetal. Of these, only Magnemite and Magneton are used by Trainers, and they typically don't even have Steel moves!
Tl;dr While Kantonian Ninetales works well, Alolan Ninetales edges it out thanks to a superior type combination and Speed.