Nothing fancy, just posting what I had written before on things I like about HanaNeji, and what potential it has in the series (although I think most of it is just in my head XD). Anyway, here goes.
I wish I could find a good fanfic for the pairing, but the idea of it started back during the Chuunin exam tournament. Although I'm not sure exactly what made me think of it, I guess it was probably something along the lines of me thinking Hanabi would be both impressed and jealous of Neji. She was the gifted one between her and Hinata, and she was probably comfortable and proud of that fact. And then here's someone who her father mentions is probably better than her. Although we don't see any reaction from her on it unfortunately, I think it'd be an interesting one, especially tying into the discord between the Main and Branch Houses.
We also don't see much of her personality, but I imagine she's determined, blunt (maybe I'm just making that one up because I like that quality), tough, competitive, and probably more calculating than empathic. With Neji's personality and distaste for authority (although it's gotten better) paired up with someone who I think wouldn't take any crap and even boss him around a bit - now that would be fun and interesting to see play out and explore in a fic. But along with their clashing interactions, at the same time I think they share the same outlook on life and toward training - and I think they would push each other to always be growing and improving.
And touching slightly on the Hyuuga politics - well, obviously this is pretty much going to be my interpretation and speculations, but I see Neji becoming head of the clan as possibly hinted by Hiashi rising above the clan structure and training Neji personally (where as before it seemed Hanabi to have a good chance for that position even if not officially - Hiashi seemed to kind of hope something would happen to Hinata (naughty daddy), which I imagine would make Hanabi heir - which points back to my interest in Hanabi's reaction to the shift). Well, this is just my guess, but I think Neji will become clan leader as part of the healing of the Hyuuga issues and not through marriage to Hinata because that's still playing by the old rules - I'd like to see Neji named it flat out which is more along the lines of Hiashi training him directly. Hinata to me never seemed to want to be clan head - she wants to prove to herself that's she's a good ninja, but I haven't seen any indication that she wants to take a leadership role, so I think she'd be happy having it passed to Neji in her stead. Again, just my speculation.
Now how does Hanabi tie in with this politically? Well, since she is also a talented Hyuuga in the making, from a writing point of view, why not have her and Neji hook up because as I already mentioned the interaction would be fun and interesting on its own accord, AND you have two strong members leading the clan AND a joining of the two houses - with neither as official heir to the clan and thus making a clean break with the old ways. Yup.
Hope that made sense, it kind of does to me, but most of it is just how I'd prefer to see things played out with taking a few cues from what's already been shown in the manga. But I think what I really like about this pairing is how much is left up to the imagination, and yet still have enough background in Hyuuga to create a rich story that fits well with the series.