We all ready agreed about the Karve so I moved on to the long boat. The rest of this post applies only to the long boat.

There is no perfect test for the long boat. The wind is all most never directly against you in the direction you want to go and over long distances it tends to change while you are trying to test. I have been consistently able to out run a sea serpent while tacking (the sea serpent follows you and also "tacks" with you) but not while paddling.

Per the testing done in the wiki:
https://valheim.fandom.com/wiki/Longship

Paddling speed in the long boat is 3.16 m/s. The worst possible speed for a headcrosswind for the long boat is 4.95 m/s. That's the hypotenuse of the right triangle 4.95^2 = 24.5. Divide by 2 for one of the sides.
24.5/2 = 12.25
Take the square root
√12.25 = 3.5

3.5 m/s > 3.16 m/s

If your forward progress tacking is slower than paddling you aren't holding the proper angle to the wind while tacking even considering fouling your turn by not raising sail. If you run longer legs before tacking you save some of the time used making turns by making fewer turns.

Because of the simplified sailing mechanics in the game (the boat is a single hit box), when you are paddling into the wind in rough seas the waves are dead ahead and the full force of the wave is slowing your progress. In rough seas with the waves on the bow only a portion of the wave force will slow your progress. Paddling in rough seas is still not an improvement on sailing in rough seas.