Hello,

Sometimes antidepressants can seem to cause depression because they give you a little more energy and now that you have energy you didn't have before, you are able to think about how hard life is, whereas before all you could really do was sleep and avoid everything.
Benzos act very quickly, and the response that they give calms you down immediately, which is why they can be so addictive. For me they make me tired, (but that's not saying much coming from a narcoleptic) and sometimes the side effect of sleepiness can be confused with depression side effects because depression causes excessive sleepiness. But other than that I don't really see any possible connection.
BUT. Everyone's body is different.

Good luck finding what works best for you!