Extracting common signal without knowledge about noise
Taking the average is a reasonable heuristic. The term “best” needs a lot more clarification because it needs a criteria.  Assuming that the signal is exactly the same on both channels is actually a strong assumption, so if you consider small perturbations to your model, say a time delay between the two channels, which is a lot more reasonable than perfect alignment, the character of the problem has changed. 

There are techniques like ICA but they work well when they do and don’t when they don’t.

If your question is of a theoretical nature, there are answers to questions like is there a common signal in both channels using non parametric statistics.

If this is a practical question, then you should look at your data very closely and see whatever else you can reasonably assume.