Yeah If Naruto wasn't cheering for her would have lost to Neji with out even putting up a fight. when you think about it Neji was the perfect opponetn for Hinata, because if it wasn't for his arrogant attitude towards Hinata and how power and skill is something you are born with and not something you earn Naruto wouldn'd have yelled for Hinata not to lose and she wouldn't have fought back against Neji. In fact I think that if it was Sakura fighting against Hinata, Naruto would have been cheering for Sakura and Hinata would have lost all motivation to fight and Sakura would have handed Hinata's @$$ to her on a silver platter
And when you get down to it, Hinatatas still is basically just going by the book of the Jyuken; everything she can do (as mentioned, she couldn't even do the 64 Palms or Kaiten) is stuff that Neji had essentially already mastered and so nothing he hasn't seen before, which would make her very predictable to him (though, to be fair, in terms of the basic fighting style, the same can be said of Neji towards Hinatatas). However, it was simply Neji's greater strength, speed, and finer technique that put him well above Hinatatas, and even more so later on due to being able to think outside the box by creating stuff like the Air Palm whereas even Hinatatas' Lion Palm, even on the wikia, is said to simply be a stronger, secret Main Branch technique (from the looks of it, though, it's more bark than bite; just using more chakra, but still fighting similarly as the normal Jyuken), not something she created herself, so again, "by the book".
Hinatatas only "pushed" Neji due to him underestimating her after she got motivated by Naruto's "cheering", but as soon as he dropped his calm demeanor and let his anger and hatred out, and started fighting seriously, he easily overwhelmed her and it required several Jonin physically restraining him to hold him back from killing her.
Nah, sakura Will not win again Hinata in part 1 because sakura doesn't have any Jutsu. Infact i don't think sakura should win again Ino. Hinata is her worst match up in part 1.
I think of Kishi should give a jutsu to part 1 sakura, like genjutsu. A weak one is enough.
There's also the fact is that Hinatatas' own "too kind" attitude (and adherence to Konoha's whole "never hurt fellow Konoha shinobi" crap) would hold her back. She would more than likely worry about "hurting" Sakura and angering Naruto by doing so (given his crush on Sakura was very open), which would most likely give Sakura a wide enough opening for a knockout. Hinatatas only really wins against part one Sakura or against virtually anyone if Naruto is right there and, in her mind, cheers for her, which he wouldn't in that match-up, or if you make Hinatatas completely OOC or something to force the match-up to be "fair" with both being as strong as they could be at the time.
Otherwise, from what Hinatatas had shown of herself overall, she has numerous internal and external factors that take her down several notches while Sakura really doesn't. Sakura's only real weakness during the Chunin Exams is her overall lack of jutsu arsenal. Obviously she's very book smart and, as mentioned, she has shown to be physically tougher than people give her credit for. Certainly nowhere near ones like Naruto, Sasuke, Kiba, and others, but enough to fight against Hinatatas the way she is.
Why is Kaiten even a good technique anyway? Realistically you will just waste all your chakra blowing things away while you are completely immobile. You don't do any damage just blow away an attack. How is that good? The attack would have to cost more chakra than what looks like this giant white cloud of energy for it to even be worth doing.
I remember reading multiple fanfics that had a more skilled Naruto or others take advantage of such huge disadvantages, like engulfing Neji with a continuous fire technique, forcing him to keep using the Kaiten to the point where he would either run out of chakra to maintain it and easily get knocked out (either from the fire technique itself or a follow up strike) from being exhausted or he would get knocked out due to suffocation due to the fire sucking away his oxygen, and even more so due to the fire being fed by the wind created by the spinning.
Heck, after the Chunin Exams, you rarely ever see Neji using the Kaiten again. IIRC, he went with the 64 and 128 palms to deflect Kidomaru's attacks rather than the Kaiten.