It's all shape. The pipe material has no effect on engine characteristics. The main benefit is weight saving. One downside is the titanium header seems to be hotter near the exhaust port than a steel pipe. Possibly because titanium is not as good of a thermal conductor as steel so it doesn't distribute the heat as well.
If you can find a copy of Gordon Jenning's book, "The Two-Stroke Tuner's Handbook" on-line (I've seen it as a PDF somewhere) it does an excellent job of explaining wave behavior in an exhaust system.
As odd as it seems electrical signals behave in exactly the same way. When I started to get into laying out transmission lines on circuit boards it all seemed very familiar because of my understanding of expansion chambers.