I didn't vote because I like them both about equally. I suppose I'll address my thoughts about Navi first...
I did not find Navi very annoying, actually. Tons of people seem to hate her, but she never really bothered me. Actually, rather than her saying "Hey" or "Listen", the only thing she did that ever vaguely irritated me was when she'd occasionally chime in and say where you were supposed to go next. That was kind of annoying, especially in a game with so many sidequests. It would be better if you had the option of asking her like in Twilight Princess.
I liked her enough as a character. Actually I found her quite likable, and some of the things she did were actually kind of cute and amusing, like the whole "Fairy Flying" sequence at the beginning.
She was also a great hint system, and I liked how she functioned a lot.
Now, Midna. I actually hated her guts throughout the first three dungeons of the game. I heard people really liked her, but when I actually saw her, I found her so incredibly annoying and rude. I thought she was a *****. :xd:
Although as time went on... more specifically around the completion of the Lakebed Temple, I took a liking to her. It started with her dialogue when you collected the final Fused Shadow, and it only continued during the sequence with Zant in Lanayru's Spring, and then throughout the rest of the game. She was a very detailed and interesting character, and the lessons she learned throughout the game were very intriguing and they made her into a very likable and in some cases admirable character.
Unfortunately, she wasn't as good as a hint system in my opinion. On both ends of the spectrum, actually. She didn't give you information one whatever you were looking at, which I disliked and frankly, I've missed that since Ocarina of Time. She only gave you vague hints or sometimes just statements about the area you were in. Then on the other hand, the second you encountered certain puzzles, she'd immediately give you an extremely revealing hint, more or less telling you how to do the puzzle before you even start it. I didn't like that.
Though Midna did have some cool powers for you to take advantage of, such as warping and turning into a wolf. I did like that.
So for me they both had their pros and cons, and I liked them both equally. Navi was a better hint system, but Midna was a more interesting character. I liked Navi's personality better, but Midna had cool powers.