In The Elder Scrolls V: Skyrim, both Honningbrew and Black Briar meads serve as stamina-restoring consumable items. Mechanically, they both restore 20 points of stamina when consumed. However, there is a difference in the side effects caused by each mead.
When you drink Black Briar mead, your stamina regeneration is reduced by 40% for 30 seconds. On the other hand, Honningbrew mead reduces your stamina regeneration only by 25% for 20 seconds. Thus, between the two, Honningbrew Mead offers a more favorable effect on your character.