Can Bruna, Light of Alabaster take my opponent's auras?
Yes, this is true for all auras on the battlefield, regardless of their controller. There's no general rule that Auras can only be attached to their controller's own permanents, so Bruna can 'steal' other player's auras.
(They'd still control them, which is relevant e.g. for Curious Obsession. This gives an ability to the enchanted creature, so you would get to draw a card if you 'steal' your opponents Curious Obsession with Bruna and deal combat damage to a player. But, as @Arthur notes in the comment, your opponent might not attack the next turn, which causes him/her to sacrifice the aura because he/she still controls it.)

You might think this is too powerful, but it really isn't; auras generally see little competitive play because they tend to lead to card disadvantage (if the enchanted creature dies, you'll lose two cards at once). And a multicolored six mana card should better win the game for you; it's supposed to be your 'finisher'. Commander is more about fun and long multiplayer games, so there this card certainly has more potential.