Was Denmark Strait a German victory?

How should the Denmark Strait operation be judged when Britain lost Hood but later sank Bismarck?

Hood's loss was severe, but the wider operation ended in a British victory because Bismarck was destroyed and the German mission failed.

The tactical shock at Denmark Strait needs to be separated from the outcome of the wider operation. Hood's destruction made the opening battle a costly German success. Britain nevertheless found and destroyed Bismarck, ending the German mission and producing an overall British victory. Judging only the exchange of ships misses that operational result. British public memory often expects every naval action to resemble Trafalgar, with enemy ships destroyed without equivalent British losses, which makes victories involving severe British losses harder to recognize.