Seeing as how Hinata is so overrated and Shino is underrated I'm going to break down this fight.
I don't know if anime is allowed, so I'll consider both. I apologise for length.
Hinata has Byakugan
Byakugan gives the user a near 360º field of vision, except for one blind spot at the back of the neck above the third thoracic vertebra. The other ability is being able to see through solid objects, and can use a degree of telescopic sight. On, the ability to see chakra. Almost forgot that one.
It does not, however, give the user the ability to predict moves, avoid them or raise their speed/stamina/etc.
360º field of vision and telescopic view will help her is seeing those insects, but it'll do nothing in helping her avoid them. Especially considering that her opponent is a strategist who comes from a clan whose insects surround an area on a whole rather than just one certain point, and are also experts in espionage.
Hinata is a close-range fighter who is not know for her speed. She has natural flexibility and while she is faster than Shino (and maybe his insects), her stamina is slightly less than his (Hinata's 2 to Shino's 3). She'll tire out quicker than Shino who is a long-range fighter than can stay out of way, overwhelm her with his insects (which surrounds a large area), tire her out and than eat her chakra.
Air Palm fouses only on one area. It'll do nothing to aid her against a type of insect that fousus on the area on a whole.
Protection of the Eight Trigrams Sixty-Four Palms takes advantage of her great flexibility and prehaps is her best bet against Shino's insects. As well as Chakra Needles. However, once Shino finds out she can use this move to kill his insects he'll provide himself with another plan. Also, because Chakra Needles uses chakra it's prehaps a horrible move to use on insects that feast on chakra.
Hinata will own Shino in Taijutsu
She most certainly will. If he didn't have his insects. Hinata would need to get past them. A difficult, but not impossible task. Taijutsu isn't good against a long-range opponent.
Hinata does not have great stamina, isn't known for her great speed and is mostly a close-range fighter. Shino has better stamina, is a long-range fighter, has the means to attack from a distance constantly (his bugs) and his latest filler has him improving in Taijutsu.
Those bugs have the ability to drain her chakra (those bees didn't) and surround a large area, which is why Protection of the Eight Trigrams Sixty-Four Palms and Chakra Needles won't aid her for long. They also have a smarter host/user.
In short: By the time she gets close to Shino she'll be too tired from being swarmed too many times. Her stamina isn't that great, her speed isn't the best and her opponent has insects that feed on chakra and attack in a large group.
Protection of the Eight Trigrams Sixty-Four Palms and Chakra Needles
The reasons why Hinata is supposedly able to win against Shino. The idea that it'll workon all insect users.
But here are a few things to point out.
-The filler showed us Aburame's Kikai>Kamizuru's bees.
-The bee's users were not known for being intelligent. Shino is at least a calm-minded strategist.
-The bees did not have the means to drain chakra.
-Those bees attack in one large swarm. The kikai attack in smaller groups. It allows the Kikai to "test the waters".
-The anime gives Hinata massive stamina she doesn't even have in the manga. How does PETSFP (Protection of the Eight Trigrams Sixty-Four Palms) not tire her out? The technique looks like it requires a lot of stamina. If it does tire her out than Shino can send out more insects.
Hinata can stop Shino's communication with his bugs
The Aburame clan can perform ninjutsu-like techniques without the use of hand seals or chakra conversion. Apart from that, Hinata will find it extremely difficult to even get closer to him.
I'm sure you guys would love a short version? Here it is. =)
-Byakugan does not predict movement or raise the user's stat. It'll help her to see the bugs, but not avoid them.
-Hinata is close-range Taijutsu fighter. Shino is long-range Ninjutsu fighter. Most of Hinata's moves drain energy (being hand-to-hand) and while she's faster than him, she has no means to avoid all of his insects. Insect Globe is known for being almost unavoidable-save for, prehaps a teleportation move. His stamina is better and he can attack from a distance, saving him energy.
-He's a calm-minded strategist. Hinata isn't.
-Kikai>Bees. Hinata killing off those bees doesn't mean Hinata>all insects. Shino is an entirely different insect user. He is an analytical strategist who has insects that can swam a large area and feed on chakra. Those bees and their users are nothing like Shino and his kikai.
-Hinata is faster, but Shino is by no means slow. She'll have a difficult task getting close to him and her having less stamina and mostly hand-to-hand moves, she'll most likely tire out by the time she gets to him.
-If she somehow manages to engage him in Taijutsu she would have lost energy (stamina) from trying to escape those bugs (something she would have done more than once as the bugs would have swamed her multiple times) and from having her chakra partly drained. Even through Shino has worse Taijutsu he would at least be at full energy. If anime feats are allowed that his lastest filler has him improving his Taijutsu drastically.
Hopefully I've provided a better reason why Shino wins. =)
She has to get close to him first. That isn't happening with such ease. Even so, Gentle Fist may do nothing to stop Shino from using his bugs anyway. He doesn't use Hand Seals or chakra conversion and they escape through the pores.
