MartinJol, as others have said, there's no reason not to get a dual-core, except maybe price (but there are really low-priced AMD dual-cores out there).
As for the argument your friend has, there are the two main errors:
1) You can't compare processors based on Ghz alone. I can't stress this enough. A new 1.8Ghz CPU beats a 3.8Ghz Pentium 4. Why? Because new processors do more "per Hz" than old processors. They're more efficient.
2) While it is true that a game can only use one core at a time (at least at the moment, Valve is working to solve that), one modern core is usually more powerful than one old CPU. For general desktop usage, two cores is much better, because multiple apps can distribute over the cores.