The cups at the drink station are a good size, maybe 16 oz. They also provide lids and straws (and a sign politely requesting you use the lids to prevent spillage). We brought mugs from a last trip, and used them about half the time. It is much easier to carry a couple of mugs instead of cups. However, I once was getting seven drinks for folks waiting for Bingo to start. The person overseeing the Drink Station offered to get me a tray from Topsiders (they were closed at the time).
If you have room to take the mugs, I suggest doing so.