The Dart Container Corporation claims that foam cups prevent carbonation loss better than paper cups (which are usually coated with plastic these days, not wax), and they have the graph to prove it.
Of course, Dart manufactures and sells foam cups not paper cups so we should probably take their claims with a grain of salt. They may be selectively presenting only the studies that make them look best.
There's evidence that carbonated beverages form more "fizz" when they're poured into styrofoam cups than when they're poured into other containers. The reason for this is that the rough texture of styrofoam (if you look closely, you'll see it's covered with tiny crevices) provides numerous "nucleation sites" where bubbles of CO₂ can form. These bubbles then rise to the surface of the drink and escape, which reduces the carbonation in the beverage.
You would think, then, that the more imperfections the container has, the quicker the carbonation would disappear. Paper and plastic cups aren't completely smooth, but I can't find any evidence that they have more imperfections than styrofoam. Based on this, paper and plastic should hold carbonation longer than styrofoam.
However, it is indisputable that styrofoam cups maintain the temperature of their contents better than paper or plastic cups. This has two effects that are beneficial for preserving carbonation in cold drinks:
1) Cooler water holds on to CO₂ molecules better than warmer water. As the water warms up, the carbonation escapes more rapidly. Since styrofoam cups keep cold beverages cold for longer, they keep the rate of carbonation loss down.
2) At colder temperatures, ice takes longer to melt. If the drink in question has ice in it, this ice will stay solid for longer in a styrofoam cup, instead of turning into water that dilutes the drink as well as the carbonation.
All things considered, I'd say that Dart and your friend are probably right: In general, styrofoam cups do hold carbonation longer than paper cups, mostly because they maintain temperature better.
More: Google Answers, The Straight Dope, How Everything Works, Dart Container Corp.