Dual-Core means the CPU has two internal processors that can run two core threads at once. ANY application can take advantage of this if it supports multi-threading.
Intel Dual-Core Hyper-Threading processors (Pentium 4 Extreme CPUs) can process 4 threads at once.
I say if you have the money and upgrading your system anyways, get the Dual-Core and start watching for Multi-Threading applications. Search for "Multi-Threaded Email Client", etc. and replace your day to day applications for ones that use multi-threading.
Currently the only game that can support multi-threading is Unreal. However there is several games in development that will support multi-threading. Even if the game doesn't support it, you OS will, and will be able to balance some process off on it. speeding up your main thread that your single-threaded game is using.
The new version of Adobe Photoshop, and new versions of email clients, IM messengers, will be multi-threaded, if not already.