As others have said, if I were to choose, Fi is the obvious choice. I didn't actually find either character to be annoying, though, at least no in excess. Each character had points where they got on my nerves, but that's sort of an inevitable result of the "helper character", and like
misskitten, the main issue is when the character forces you to hear what they have to say, or gives you an annoying sound to indicate they have something to say (both of which have been done by either character). I enjoy both characters a lot, and I do think the rage against them tends to be blown a little out of proportion. It's valid, but out of proportion. Still, if I were to pick one as the most annoying, I'd have to choose Fi because she's a lot more invasive than Navi.
I like Fi's voice, sounds robotic and fits the way she talks. The only thing I found annoying is when she reminds me that the batteries are about to run out. -.-
Yeah, that irked me a lot too. Actually, what was worse for me is the "you're low on hearts" notifications, because she would never stop. This is a game that's supposed to be challenging, Nintendo, so don't you think it would be a good idea to not add insult to injury and continue punishing us for losing hearts?
Everything's wrong with being so obvious to the point of insanity. Say you just hit a timeshift orb. Fi then comes up and says "Master [name], readings indicate there is a 95 percent chance that you have hit a timeshift orb [...]". Tell me that isn't annoying. If you do, you are either very tolerant of people, or you must be a robot yourself! Her 'percent calculations' are nothing more than a waste of time and a way to fit computer jargon into a medieval game. There was absolutely no reason for Fi to be as annoyingly obvious as she is. What need have we for her to tell us that we just solved a puzzle, the result of which we knew beforehand? Not even Navi does that kinda thing.
With regards to the timeshift orb example, you're oversimplifying it. She first gives you that notification when you first encounter said object, and clearly new players would have no idea what they actually are, so Fi's info is useful, especially in explaining the time aspect, as a player isn't going to be able to figure that out on their own, even if they can figure out the gameplay. I believe she did mention it a few times later, but if I recall, each one was also along with other information regarding the situation and how the timeshift stone specifically affected it in that circumstance. It's not as blatantly useless as you're making it out to be, and I suspect that you were like me and were made familiar with the Timeshift Stones' concept long before playing the game, but that's just not the case for everyone and a game can't be designed under the assumption that everyone kept up on pre-release coverage.
As for your complaints about percentages, I don't understand why that's something to complain about. It almost sounds like you're equating it to being an actual analysis to help the player, but it never was. It was Fi's particular speech pattern and it was only constantly repeated because that's part of the character. It's just one bit of Skyward Sword's high-quality dialogue.
I will definitely agree with you though that there were a handful of stupid design mistakes with Fi, but I don't think the ones you've listed are them...