Mostly, performance will vary by how the game is compatible with the emulator. That said, the wii was a single core system, and I believe that, by now, they added some multi-core compatibility option (just as much as PCSX2 has the MTVU speedhack option, allowing the emulator to run with virtually any number of cores rather than just 2, as the original PS2 sported).
As long as you're not trying to play at 5 times the native wii resolution and the game is compatible enough with the emulator, you'll be fine with a dual core