I am curious about a certain part of this quest, where the player has the option to use Intimidate or Persuasion skill. I would like to hear what the consequences are.

I will tell how i did the quest, maybe other players will remember it and can share their experience.

The Quest is given by the Altmer Queen in Auridon, and I had to talk to the Khajit Captain Jimila to take me to the next Island. Before she took me there, she offered a drinking contest between me and her. If I win, i get my private cabin on her ship, if she wins I have to do her laundry for one week, as far as I remember. I accepted the challenge, the screen turned black and i appeared behind some rocks nearby. The captain was gone. Obviously I lost. I traveled to another city where she had her ship (The Crowler) and talked to her. She also seemed to have a blackout from drinking too much, but told me that she thinks she won. Now I had three dialog options:

[Intimidate] Shout at her that she is a liar and I won.
[Persuade] [Lie] Tell her that I won and she did embarrassing things while drunk.
Admit that you lost.

I checked online for more than 20 minutes about consequences, but couldnt find anything. On the one hand I actually want to admit the truth and find out how the quest would continue; and on the other hand using the dialog skill usually rewards the player.
In the end i decided to say the truth. Her reaction was something like: okay, are you ready to take the ship now? Quite disappointing.
So I would like to hear what difference it makes to use the skill at this point.