For what it's worth, I have seen the very best relic bows turn up in speedruns on YouTube (though the original videos have since been taken down and live on only on my hard drive). So if the speedrunners are using them, I assume they must have some value. Though I don't know enough about bow damage values to judge.
Relic bowguns, on the other hand, never seem to show up in speedruns. It's usually the Gigacannon, Griscannon, or Furia Sedition. So if there are some worthwhile bowgun relics, nobody's using them to break any speed records.