I think before doing A/B testing it is important to clarify the objective or hypothesis of the test so you can understand how to interpret the results and therefore what changes you should make based on your findings.
You might find that the effect of changing the button colour to help improve conversion rates (which is usually the case for call-to-action buttons) is not necessarily due to the effectiveness of a specific colour (e.g. blue versus red), but rather the properties of that colour (e.g. bright versus dark).
The two different processes that you have described has the potential to result in two completely different conclusions depending on what the optimal colour might be. For example, if red happens to be the most effective colour by a large margin, then regardless of the way you run the test you would probably expect the same result.
On the other hand, if red is only slightly better than all the rest of the colour but blue is much better than yellow, then you might for one week happen to see more clicks for blue and so you pick blue to compare with yellow next, coming to the conclusion that blue is the best colour. You might not be able to conclude that red is the best colour with a side-by-side comparison, but you can probably eliminate some colours that definitely should not be considered.
Consider the case that red buttons are better for one type of transaction or user flow, and another colour is preferred for another type of transaction or user flow. How can you determine the best overall colour to choose (since you will probably not use both or change them depending on context). In this case you may find yourself comparing red with blue for one type of transaction and then also for the other type of transaction.
I guess the point I am trying to make is that you should try to set your A/B tests to be as simple and definitive as possible, because the more variables you introduce (even if it is just more colours) the more likely it is that some other factors will complicate the interpretation of the results. It is hard to control all the factors to make sure that the only factor that has an impact on the user behaviour is the one that you are testing, and to attribute that effect to the variable you are introducing.