When testing multiple hypotheses on the same set of collected data, we want of course to correct for the increased likelihood of false positives from multiple tests.
So far I've always used the Holm-Bonferroni method to adjust the Family-Wise Error Rate (FWER) to $\le 5\%$.
However, there's also the Benjamini-Hochberg method. From what I understand, it can be used to fix the expected False Discovery Rate (FDR) across all performed tests at (let's say) $\le 5\%$. It could thus allow a $> 5\%$ chance that at least one of our results is a false positive, but offers a much higher power as a compromise. In addition, I believe that it (like Holm-Bonferroni) doesn't require any assumptions about the the test themselves being dependent or independent. (Please correct me if any of that is false.)
I'm now wondering, from a very practical standpoint, when is it acceptable to use Benjamini-Hochberg to control FDR, and when must I strictly keep FWER $\le 5\%$?
For example, let's say we have an experiment and compare a number of interventions each against the baseline. They will be compared regarding several dependent variables. So we'd have a number of Hypotheses (e.g., $H_{ij}$: Variable $i$ differs significantly from the baseline in condition $j$). What factors now influence whether I should focus on FWER or FDR?
(If that helps, I'm in Human-Computer Interaction. As a comparatively young field, we unfortunately don't have strong statistics traditions or best practices to fall back on / they are not yet necessarily reliable)