I just want to know if AMD or Intel processors would have any advantages when it comes to running a DAW (specifically Abelton Live 9). I already know Abelton and other similar DAWs like to use up RAM but wasn't sure if they run better on certain CPUs.
Nope, a lot depends on the mobo, some mobos have more latency than others, that's just how it is, in general, simpler (cheaper) mobos have less latency.
And if you're using Ardour, you can also use the power of AMD graphics cards or APUs to do DSP processing and to speed up realtime processing. Ardour has by far the best audio quality because it is 100% floating point precise, unlike any other DAW. It can use AMD GPUs to offload a lot of processing from the CPU, and with newer AMD graphics cards, it can use the DSP that is built-in in the graphics card for processed reproduction with less CPU load. Ardour basically is now limited to only the hardware latency, as the audio APIs are externalized, and with JACK, you basically have a near-zero API latency on non-proprietary locked down audio hardware. So you'll have the best low latency there across the board, but with CoreAudio, it should perform very well in terms of latency also. Ardour doesn't support DirectAudio, which is very bad for latency, and it doesn't directly support ASIO, only via a compatibility layer on JACK, which means that there will hardly be a latency gain there also, but hey, the ASIO and DirectAudio APIs are now 20 years old, they haven't been able to keep up with low latency for quite some time now. Latency is in no way influenced by the CPU, but it's influenced by the mobo and the API.