None.
USPC stopped making Aristocrat stock a handful of years ago. Those decks were the last. to be more accurate, they stopped creating pasteboard stock in that manner - they don't actually make the paper, but they do make the "paper sandwich" that forms the pasteboard used to make cards. They can set thickness, level of pressure, humidity levels, emboss them, coat them, etc., but the flattened tree pulp comes from paper mills.
Tally Ho decks were made with a slightly stiffer version of Aristocrat stock, back when they stopped making Tally Ho stock. But you'd be looking for Cincinnati-made decks. But honestly, I've never felt cards like the Aristocrats reprints - not any modern decks, anyway.
A few decks came out in the last few years stating they were made on Aristocrat stock - but the reality is that USPC will allow people to give all kinds of names to their products. Ever heard of "Apocalyptic Finish?" There's a deck that has it. (Diamond Jim Tyler's Doomsday Deck. But it's just another way of saying "embossed with Magic Finish.") How about "Premium Finish" - what kind of finish is that? (It's another embossed card with Magic Finish - specifically, white Arrcos by NY Magic Project and the Blue Crown.) I could call my next deck's stock "Angel Hair Stock" if I felt like it. Propaganda cards from Theory 11 are "909 Edition" - what does that even mean?
Right now, USPC offers two stocks - Bicycle and Bee Casino. They're measured by thickness, and they're in a range of thicknesses, not one specific thickness. The ranges between the two stocks overlap - a thick Bicycle deck can be as thick as or thicker than a thin Bee deck...
The only caveat I can give you is that their best clients get their best service and products - it's not impossible to have them make Aristocrat stock again, but it's not on the menu. But for the right person and the right amount of cash, they'll put it on the menu, I'm sure. They're a business, like any other, and they're in business to make money. For some guy making his first Kickstarter deck in the smallest-offered print run, they're not exactly going to jump through hoops for you. Ask them for a six-figure-plus print run, they'll set the hoops on fire first!
I'd be interested in seeing a company like Legends or Expert come up with a stock that's comparable to the old Aristocrat and Tally Ho stocks...