An earlier post made me think that perhaps you can only complete one or the other quest. The post reads:
In my latest game I am unable to get the promotion to "Great Wyrm" because Deftclaw Redreaver does not acknowledge that I have done so (and yes I have the sword equipped when talking to him). The only thing I get from him upon entering his cave is "Tahnks for the help!" (which I believe stems from the Dragonbane flower quest). I do not think he ever even gave me the quest to kill Jericho or whatever his name is. I did get the quest to kill all of the dragon hunters and I killed every one of them inside and outside (though they immediately respawned) but it does not register with him that I have done so.