for most of these stations, its more about if DL utilizes common-use gates or if everything is Delta proprietary. Its not necessarily the whole station or nothing at all, but having common-use gates tends to have a greater chance that you'll see cardstock.

Vegas is entirely common use, and I think RDU is also, so you'll get the cardstock there. Some of the Seattle gates are "Port" gates (Port of Seattle) so you'll see cardstock there, but not at the other ones. The LAX gates at TBIT have cardstock, but not at Terminal 2. The new terminal at PHX has them. ATL F concourse gates has them, and a few of the E concourse gates (E34 & E36 I think) down where B6 and Spirit have a departure or two. The rest of E became all Delta gates once F opened, so they only have the flimsy paper now. I have even seen cardstock at PIT at 1 or 2 of the gates further down on D concourse that ACAA owns (not D76 or D78 though, which are the closest gates to the tram that DL uses exclusively).