The choice of wire largely depends on the current. You may think that the wire acts like water pipe. The larger the current, the thicker the wire. In my opinion, there should be no advantage to use thicker wire for connecting the battery if you have thinner one in the circuit. 12AWG should be enough for 1/8 RC.
This is only my opinion and may not be completely correct. I can only tell you that I have tried both Big6 10AWG, Big6 12AWG, Tekin 12AWG and mix of them. No obvious difference on performance but Tekin 12 AWG should be lighter than Big6 wire. In fact, I have bought 50 feet of Tekin 12AWG wire already...
If your soldering skill is not good, stick to 12AWG. It is hard to solder 10AWG to the Tekin ESC neatly. Some high hand here screwed the ESC with Cow {banned} Soldering Point