A few things. There's a new skill tree, Fugitive, inspired by Old Hoxton (now just Hoxton, as New Hoxton is now Houston).
The tier bonuses have been scrapped in favour of Perk trees.
A lot of abilities have been changed, replaced, or repositioned.
There is now a Death Wish difficulty level with tougher and better cops, plus super-tough Bulldozers. And of course, some heists are extremely hard.
Cloakers are back.
LMGs, sniper rifles and melee weapons were added to the game. Plus a crapload of extra weapons, mods, and inventory spaces.
You can choose which songs play in-game (both menus and heists).
Rats is now non-rushable.
Stealth is much harder.
There are xp bonuses and reductions for each heist, depending on how much you have played it.
The Infamy system (still in construction), that allows you to reset your character to gain advantages.
A lot more heists, both loud and stealthy.
And I think this is the most important stuff.
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BTW, new Xmas update, "The White Xmas Heist":
http://overkillsoftware.com/whitechristmas/
A free (and hilarious) Christmas carol Payday style, and a new free heist with its masks and achievements. We'll have to rescue Vlad's Bosnian Norwegian brother-in-law pilot, plus his huge shipment of pure Colombian coke, of course.