Power-up skills are buffs (with a slight visual change) rather than genuine transformations. Stuff like Super Saiyan, Kaioken, and a few variations. The game handles it for NPCs by making them scripted for the most part. Like, you'll beat up Vegeta and then he'll go Super Saiyan, etc. The game's time-travel shenanigans explain away some missing transformations, too.
Because it's scripted these transformations can only happen in specific modes, not regular PvP battles. NPCs or players in regular PvP battles will never be able to, for example, use Frieza 1st Form, power up to 2nd form, 3rd, etc. It will be Frieza 1st form, or whatever you select at the start, with nothing else for the duration, save for the power-up skills mentioned before (if the character has them equipped).
I'm not sure how the battle system compares to previous Dragonball Z games, but from what I gather those were more traditional fighters, whereas DBXV is more like a brawler/RPG/quasi-MMO hybrid. There's much more focus on group battles, character stats and equipment/items/crafting, interacting with the environment, and specific/unexpected events in missions, rather than simply "reduce one opponent's health to 0." The Parallel Quests (3 players/NPCs vs a series of NPC scenarios) in particular are a huge aspect of the game, where levelling, equipment, and new skills/strategies are learned, all of which help the player take on the story missions.
Giant Bomb has a pretty good Quick Look of the game if you want a better look at it; most of the systems and gameplay are showcased.
I'd say the bottom line for Dragonball Xenoverse is, if you have any love for Dragonball Z, this game is for
you. Aside from server issues and some RNG annoyances, it's a really fun, compelling take on Dragonball Z, not to mention a promising start for a new line of games. There's a lot of little touches that mark it as a labour of love, as well as a great deal of content to chew through if you're so inclined.
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