Hm. I suppose it would depend on what you want from an island vacation.
Allow me to put it this way: although all three of those regions are tropical in nature, their cultures make them vastly different. In Alola, the people are highly friendly and eager to share their culture with outsiders, in part because the tourism industry is the biggest contributor to their economy. As such, if you’re the sort of tourist who enjoys exploring historical landmarks and observing regional culture, Alola is an excellent choice for a destination.
Meanwhile, the Orange Islands also rely on their tourist industry, but it shares a lot of culture with its neighbors, Kanto, Johto, and Hoenn. Thus, people travel to the Orange Islands less to take in the regional culture and more to enjoy a tropical island paradise. There are plenty of resorts and relaxation spots throughout the archipelago, and the less-inhabited islands, such as the Seven Grapefruit Islands, are tourist destinations centered around the region’s agricultural industry or its unique gym circuit. (I would highly recommend the Orange Islands’ fruit tasting tour, for example.)
Finally, the Sevii Islands are far less inhabited than the other two regions, and due to that and its general isolation, the locals are less friendly towards outsiders. You’ll find it harder to partake in local culture or find a resort outside of Seven Island. Even then, Seven Island is more of a destination for trainers due to the Battle Tower, rather than a general tourist spot. (Seven Island is also home to the Tanoby Ruins, but that’s a highly sacred site to the Seviian people. Thus, it’s discouraged for most people to enter them.) On the other hand, the entire island chain features highly rugged territory, beautiful swaths of wilderness, and the best hot springs in Japan, so it’s worth exploring for those who enjoy hiking or training in rigorous environments.
Additionally, if you’re a trainer who likes transitioning from a vacation to your next big adventure, keep in mind that only the Orange Islands has a gym circuit. Granted, each gym is a bit nontraditional in nature. Rather than simply a battle, you’re required to participate in a challenge of skill before you’re permitted to face the gym leader. There are four gyms in all, culminating into a battle against the reigning champion. Thus, the Orange Islands may have something fairly close to the gym circuit you’re used to, but at the same time, it’s a vastly different experience from the traditional gym system.
Alola has its own trainer’s circuit in the form of the island challenge, but this is more of a local concept. Outsiders can participate, but they’re less encouraged to do so. However, the Pokémon Association is in talks with Professor Kukui about setting up an actual gym circuit in the region, but this won’t happen for a few years and is therefore less useful to you.
The Sevii Islands, as noted earlier, has no gym circuit or equivalent trial of their own; besides training in the wilderness, the only facility for trainers is the Battle Tower on Seven Island. Of course, also as noted earlier, the region is still filled with excellent training spots.
In short, if you’re the sort of person who just wishes to relax in the island sun, go to the Orange Islands. If you’re looking for a full tourist experience, try Alola. Finally, if you wish to go on a full-scale adventure in the wilderness, take your team to the Sevii Islands.
May your vacation be highly enjoyable, regardless of what you choose, anonymous!