I am analyzing an experiment where I have samples from multiple regions of the brain, in a number of different conditions. We are only interested in differences within brain regions, not between them.

Is it recommended to combine the tissues into a single model, or should they be analyzed separately?

My initial thought was that increasing the number of samples should provide a better estimate of the mean-variance relationship, and increase the power to detect differences. When comparing the two approaches some regions seem to gain power to detect differences, while other lose power when combined into a single model.

It is a matter of judgement. If the regions are very similar in expression and the samples have been collected and processed at the same time as part of the same study, then you might benefit from analyzing them all together. If the regions are quite different in expression, or differ in variability, then it is better to analyze them separately.