Wizard, by a wide margin. Invisibility laughs at a mere class skill bonus to stealth, and whereas rogues never get any abilities anywhere near impressive enough to pull off that sort of Carmen Sandiego stunt, for a wizard with higher-level spells it's very doable.
honestly when the whole system is built against all forms of stealth... good luck stealing a building even at level 20 and even if it's a freaking small outhouse. short answer... not likely.
Third option would be a seeker archetype sage wildblood line sorcerer.
Wizards are going to do the stealth gig better than most. They have no ACP and have dozens of ways to beguile and escape. Arcane Trickster is a way to meet in between, vivisectionist/wizard is a pretty cool magical combo that can go into arcane trickster. Never seen Mouse though so I have no idea what you want out of him.
Rogues do nothing that makes them better at stealth. Alchemist have mutagens and extracts. Why would you think rogues would be better at stealth? The ninja's vanishing trick is okay, but not great if you want something that'll stick around. Especially not if your dipping.
the best phantom thief is a bard with the vagabond child trait. if you build a phantom thief, ask yourself if this class has abilities that would have greatly helped you in a college panty raid. the panty raid in college is the entry into the quickest of forms of burglary.
rogues having nothing that augments stealth beyond making it a class skill and light armor proficiency, which necessitates a dexterity investment and comes with low penalties.
the ninja, which is a rogue archetype. adds 1/3 of their ninja level to stealth checks, and may vanish a limited number of times per day with a really short duration. they get it as a swift action, but the limited duration is impractical for even the quickest of panty raids.
by level 4, the bard gets blur, which lasts 4 minutes. it allows stealth while moving, by providing concealment and making you a living mirage. it also doesn't fade in combat. no amount of stealth bonus is viable without concealment, and with proper timing, 4 minutes is plenty of time for a brief panty raid. a 14 or better cha makes this usable twice a day at 4th level. a third use comes at 5th. for 5 minutes apiece. 15 minutes split in 3 5 minute increments is plenty of time for a quick heist in the hands of a player who knows the basics about their mark. and way too much time for a quick college panty raid, assuming you don't take 20 searching every underwear drawer.