In the Naruto franchise, children are trained to protect their villages in a similar fashion to the way children are prepared to enter the Hunger Games. The difference is that Naruto's kids are trained to be soldiers while in The Hunger Games, the kids become entertainment and sacrifices for the masses.
Some fans might compare the experience of the Chunin Exams to that of The Hunger Games. The kids form alliances, battle one another, and even compete in an enclosed arena under the watchful eye of older ninjas — though they aren't supposed to have to battle to the death. If Naruto and his classmates found themselves in the Hunger Games instead of their regular Chunin Exams, not all of them would be able to survive, despite their shinobi skills.
Hinata
While Hinata becomes a powerful shinobi in Naruto, she's still an incredibly gentle person. She only initially trains to be a shinobi because it's what's expected of her, and then, to prove that she has what it takes.
In the arena, Hinata would be willing to fight others, but when it came to killing fellow teenagers to stay alive, she'd likely try to avoid it. Her Byakugan would allow her to avoid the fighting for a long time, but eventually, she'd have to face off against someone who would likely be more powerful than her.
Tenten
Though the audience doesn't get to know her very well, Tenten is a great close-combat fighter in Naruto. There's not a weapon that exists that she can't figure out how to use. She isn't, however, a very powerful fighter, which means she would definitely need to align herself with others in the arena.
Tenten is absolutely the teammate who feels responsible for others, though, so if she did make alliances, she would find herself constantly helping her allies and never doing what was best for herself. That would be her undoing.
Rock Lee
Rock Lee is an incredibly enthusiastic fighter. He loves a challenge, and he never backs down from a fight. While that's admirable in a shinobi, it could get him into trouble in the arena. If he ended up facing off against someone like Gaara, for example, for his life, it's likely Gaara would be able to overpower him and win.
Lee is also someone who always wants to help his friends, which is, again, admirable under normal circumstances. That means that like Tenten, in the arena Lee would probably get so bogged down with helping his allies that he would end up the one targeted by others.
Neji
Neji definitely has the kill-or-be-killed approach to fighting that a tribute wants to survive the Hunger Games arena. Neji did, after all, almost kill his cousin Hinata in their Chunin Exam match-up. But that isn't necessarily enough to make it through the games.
Like Hinata, Neji would have the Byakugan to avoid stronger opponents, but also like Hinata, there are a lot of people who could easily overpower him, like someone of Sasuke or Naruto's power level. Once Neji had to go up against one of them, he would be done.
Ino
Ino is one shinobi who is seriously underestimated. A lot of her screentime in the early anime is devoted to her crush on Sasuke, her obsession with her appearance, and her rivalry with Sakura. Under all of that superficial focus, however, is a very smart shinobi who can literally get into the minds of her opponents.
In the Yamanaka can, psychic abilities are the norm. Ino is underutilized in Naruto, but that doesn't mean she couldn't use her abilities to last quite a while in the arena. The trouble is, Ino doesn't have a very deep chakra reserve, and eventually, she would burn out and be taken out of the competition.
Sakura
Like Ino, Sakura is incredibly determined and competitive but also very focused on shallow things instead of her actual shinobi training when the series begins. Sakura actually begins to focus on her training long before Ino does, which is part of the reason she could edge her out in the arena, despite Ino arguably having a more effective power set.
Sakura has an advantage over a lot of her classmates as well. She's strong enough to knock someone out with a single punch without using her chakra. She's also extremely adept at seeing through hallucinations, so it would be hard for someone to catch her by surprise, and she is an accomplished healer. However, Sakura still isn't the most strategic of shinobi and could be outsmarted.
Choji
Choji might not be someone a lot of fans would think of as a contender in the Hunger Games. He's more gentle than some of his shinobi classmates, and he has a reliance on large amounts of food to replenish his chakra levels after using his abilities. If food is scarce in the arena, that becomes a weakness for him.
However, Choji proved himself capable of doing something most of his friends couldn't — kill someone he loves. It took just about everything out of him, but it was Choji who led his teammates to take on the resurrected form of their mentor with his size-change jutsu and his butterfly form. Choji would be able to make it pretty far as long as he was protecting other people.But when it became a one-on-one fight, there's a good chance he would fall.
Naruto
Naruto might be the most powerful shinobi of his generation, but he doesn't end up as the last one standing for one simple reason: Naruto doesn't kill his enemies. Fans might joke about him spending more time talking than fighting during his confrontations, but that's exactly what he does.
Naruto is always willing to give people another chance. He would rather try to talk them into putting down their weapons and giving up a fight than he would use his power against them. That's not the best strategy in a fight to the death, and an enemy would eventually interrupt his talk-no-jutsu with a fatal blow.
Sasuke
There's no question that teenage Sasuke wouldn't have hesitated to kill someone else to keep himself alive. He does it during the Chunin Exams when his cursed mark from Orochimaru is activated. Sasuke is also powerful enough to outlast most of the competition.
The trouble is that, despite being quieter and more serious than Naruto most of the time, Sasuke can be just as impulsive. He would only think of the games as a fighting competition, not a battle of wills, and strategy. There's still one more person who could outlast him.
Shikamaru
Though Shikamaru wouldn't want to have anything to do with the Hunger Games, he would win it all. He might not have the chakra reserves of most of his friends, but Shikamaru is easily the smartest of Naruto's generation.
Shikamaru knows when to use his abilities to his advantage, and when not to. He also is able to think several steps ahead of his enemies, understanding just how and when to move against them. He wouldn't like having to kill people to keep going, but he would do it.