The "paper" tickets never went away. In certain places and circumstances, plastic cards are now used as a ticket medium, but not in all.
Tickets bought from the
Disney Store are a thin plastic card, rather like a
WalMart gift card, but a little thinner.
Tickets bought at WDW ticket windows and resorts are tyvec (paper), but they can be coded onto your Key to the World (KTTW, the room key) card, which is a thick plastic card, like a credit card or bank card.
If you buy a package that includes tickets, the tickets are automatically encoded onto your KTTW card, which is thick plastic.
Tickets bought from brokers like Ticketmania, Maple Leaf, etc., are tyvec. However, is is generally possible now to have those tickets coded onto your KTTW card, too (it wasn not always so).
The tyvec tickets are just as durable as the plastic tickets. In fact, they are better in some ways, because plastic can build a static charge from rubbing in a pocket or wallet that can demagnetize the magnetic strip, and plastic cards can crack if sat upon, while the tyvec tickets don't crack and build up far less static from friction than plastic.
I have also seen the ink used to print on a KTTW card scratch off, while the ink used to print on the tyvec tickets will not. This might contribute to the longevity of APs, which are always paper no matter where you buy them (only AP vouchers bought from mail order or Disney Stores are plastic, the actual passes are tyvec).
