I have a question about the best approach for analyzing an RNA-Seq experiment using DeSeq2. My experiment involves three different tissue types (named C, G, and P). I want to find out what genes are enriched in/unique to  each tissue in comparison to the other two tissues.

What I was not sure of is which test in DeSeq2 is most appropriate to use: pairwise comparisons between each tissue or using the likelihood ratio option. 

Right now I have just been doing pairwise comparisons of:

C vs G,

C vs P,

P vs G.

Then I took the DEGs and looked for overlap in the gene lists using Venn Diagrams in order to get genes specific for each tissue type... For example:

100 genes are up-regulated in tissue type C in comparison to tissue G.

200 genes are up-regulated in tissue type C in comparison to tissue P.

Of these 300 genes, 75 are in common across both lists and therefore are potential "Tissue C specific" genes.

Is this the best way to go about this type of analysis? Or would using the Likelihood ratio test in DeSeq be a better option? My confusion with the LRT test is how do you go about finding genes that are up/down-regulated in each particular group compared to the others? 

Essentially how do I get at asking what genes are up-regulated in Tissue C vs. Tissue G and Tissue P... And so on for each of the other tissues...

I read through the vignette section for LRT tests and also looked on bioconductor previous posts. I found some posts with similar questions but after reading through them I still was confused on the best approach and would love any insight someone more experienced may be able to offer! Thanks :D

Performing pairwise Wald tests and looking at the intersection is my preferred way of specifying that A is different than B and A is different than C.