Suppose I have RNAseq data for three conditions, A, B, and C.  I can take all the data I have, build a sample table, feed it to DESeq, and use results(dds, contrast=) to compare each set of conditions.

Alternatively, I can take only the data for each pairwise comparison and run DESeq for each pair. .

I've tried this, and the results are fairly different between the two approaches.  Only about 60% of significant genes overlap with my data. 

How do I interpret this effect?  Obviously, the data I'm not contrasting is still going to affect the linear model being created, which will affect the results table.  But is it making the model better or worse?  Which do I trust?

This is a frequently asked question (FAQ) on the support site, and it's also one of the FAQ with a response in the vignette:

https://bioconductor.org/packages/release/bioc/vignettes/DESeq2/inst/doc/DESeq2.html#if-i-have-multiple-groups-should-i-run-all-together-or-split-into-pairs-of-groups

Let me know if you have further questions.