GBARunner3 is still under development, but in any case DS phat/lite does not have enough power and RAM available to play some games, and the sound is still worse. But with an expansion pack or a Supercard SD in the gba-slot you would have 16mb and 32mb of additional RAM respectively: it would be a great help for sound performance and compatibility with more demanding titles.
Ultimately, in your case a GBA flashcard is the most effective solution. A Supercard SD is cheap and two developers have recently been perfecting two custom firmwares for this model, significantly improving it: on GBATemp you will find their projects.