Personally it feels like it relys on both to an equal degree. I've read in a lot of places however that dual core CPU's are suffering in SWTOR (The now fixed PVP responsiveness issue for example).
I did a wee experiment there. My machine is an i5 2500 and my old machine that my Girlfriend uses is an AMD Pheom Tri-core 8750 (Black Ed and overclocked to 3ghz). I swapped my graphics card (560Ti, 1gb) between machines, as well as my spare - a radeon 3870HD. Result being that the Phenom with the Ti runs a little slower than the i5 with the 3870, but not a whole lot (min FPS phenom with Ti - 23, Radeon - 13, min FPS i5 ti - 43, Radeon 19). Ok it's not a perfect example. But even a good quad core cpu with a card barely above min spec struggles, basically.