Care for the two variations is more or less the same, anonymous. The only differences is that Alolan vulpix are generally seen to be slightly harder for the following reasons:
1. Grooming. Their cloud-like manes and tails capture more debris than the neatly curled manes and tails of standard vulpix. Thus, Alolan vulpix require more vigorous daily brushing to maintain its peak mental health. Moreover, its fur only gets harder to groom after it evolves, not only because an Alolan ninetales possesses thicker, longer, and more unruly manes and tails but also because Alolan ninetales are far more fickle than standard ninetales.
2. Personality. While standard ninetales are far more hot-headed (forgive the pun) and much easier to provoke, they’re also easier to predict and understand. That is, a standard ninetales will never attack for no reason. However, although it’s famed for its calm demeanor, Alolan ninetales’s affinity for the fairy element may make it more mischievous and prone to trickery. It’s said that you should never lay a hand on a standard ninetales … but you should never turn your back on an Alolan one.
By contrast, however, the variations of vulpix are nearly identical, although the Alolan one tends to be calmer and easier to please.
3. Evolution. The ice stone needed to evolve an Alolan vulpix into ninetales is extremely rare, available only in certain parts of Alola and the Arctic Circle. By contrast, fire stone is readily available, so if your standard vulpix wishes to evolve (or if you wish to evolve your standard vulpix), all it takes is a visit to a reputable stone dealer.
All of this isn’t to chase you off the idea of raising an Alolan vulpix, anonymous. Both forms make for excellent pets and partner pokémon, and if you prefer a calmer pokémon or one of the ice element, the Alolan variation is an excellent choice. (At the very least, it won’t set fire to your possessions or home.) It’s just that overall, it’s a bit more of a challenge to raise, especially if you’re considering evolving it at some point in time.