Well, the key differences are that I liked the characters, and you seemingly didn't - so you may not take what I say seriously, but please, hear me out.
Firstly, I didn't find Rinoa annoying - she's one of my favorite characters in FF. I also noticed the chemistry in the relationship between her and Squall early on in the game, even when they are having their (deliberately) childish fights, which is a given sign in fiction (and real life in some cases). And yes, Squall was "silent", but that was because of his background - he'd been let down so many times in life he had given up expecting anything was going to get better.
It may seam like I'm starving for attention here, but I am just trying to help you understand my point - I actually went through a "Squall" like phase when I was younger (before I played FFVIII) - my life wasn't anywhere near as bad as Squall's, but a lot of things where happening, friends where leaving I was just not very good at making friends - I identified with Squall because of this, I have said this before, but he is my favorite FF character.
Squall is "silent", but we know from his thoughts that he does want to be more open, deep down there are many scenes that without these insights that would make Squall seam a much more uncaring person than he actually is.
Squall doesn't just "suddenly" fall in love with Rinoa - it happens gradually, like most Medias with a storyline FFVIII doesn't have a set timeline, so we don't know how much time has past between their first meeting, and time he acts more caring. Further more, he didn't begin to love her when he was in a coma either - it had been developing through out the game. There is definitely passion during the dance scene, He seams generally concerned for her safety when the Igniouns(sp?) have her cornered, just before the battle starts (even though, to me, they really don't look like they are make that much of an attempt to attack her - infact they look somewhat playful

) After the battle Squall is initially shocked by Rinoa's reaction - he says it's because he assumed she was "used to battles", but I think it's because he isn't used to people displaying emotion in front of him. No one, not even Quistis (who is revealed to have had a crush of sorts on Squall in the past) has shown this much in front of him. His demeanor then changes, he reassures Rinoa, that everything is ok and basically tells her to "stay close to [him]" There is a touching moment in the battle coming up where Rinoa states that she's alright if Squall is by her side - After that battle Squall is almost killed, and Rinoa reacts more directly and personally than anyone else (admittedly the only other people present are Irvine, Seifer and Edea, and none of them are going to react!) If you look at Squall during that scene - he seams to be more focused on Rinoa that anyone, or anything happening in that scene.
In disc two - there are some optional scenes of them together. Squall is still learning how to act around people, but the two of them seem to have neutral understanding of how each other are now, Rinoa makes comments on how Squall is "expected" to act a certain way. When there is a ceremony for Squall becoming the leader there is a very romantic scene between him and Rinoa - we see how close they are now becoming, and once again Squall's thoughts are there to help us understand that Squall has the potential to change and Rinoa is helping him do just that. She seams to be pushing him to talk about something, just to see if he will open up, he of course doesn't, but his thoughts show us, that he is simply scared that if he does then it will all be for nothing - nobody stays around Squall. He's not the kind of person to be loved, but why would he care so much about some one, he supposedly doesn't care about.
I also think the infamous orphanage scene (which, I absolutely loved, but I have a whole article in writing as to why) was semi instrumental in getting Squall to open up more, he has time to think about this even in game time, he had lost so much more than he ever realized, and now sees that every one (sans Rinoa) went through a similar time as him when he was younger, I think he felt a bit more assured then. I also think it gave him more strength to open up with Rinoa.
Then the coma does take place - I didn't find his actions a change in character, I saw it coming. I really thought that Squall was falling in love with Rinoa as far back as disc 1 although I think that might have been more "I find her interesting" type of love, at first, but as time went by (remember we don't know the exact timeline) they got closer, and his love for her developed, he just needed to accept that he felt something for her, and get over his fears of losing someone again. You basically have to read between the lines sometimes - this is a shortened version on why I found Squall and Rinoa such a compelling couple, I may right a full article on it one day (it will take a while, so don't expect it to be instant - I do so many projects at once).
Thanks for reading this, I'm sorry if it was long, but it needed to be.