So this is kinda not what you think it is. It's not which is better, it's do you think if Bella, Edward, and Jacob went head-to-head with Katniss, Peeta, and Gale, which team would win? And it would be a fight to the death, real death, not undead. So if The Hunger Games characters turn into vampires, they aren't dead dead, so Twilight wouldn't have won.
Yeah I'm definitely betting on Hunger Games in this fight, too. I'm probably biased, but even still.
The characters from the hunger games have really suffered. Particularly Katniss and Peeta, who've been through senseless torture and cruelty only to stand up and make some gut-wrenching sacrifices in the name of vengeance.
Really, I imagine that Edward and Bella would be jumping over each other to sacrifice themselves for the other like limp sausages. Then Jacob would throw off his shirt and bark only to get shot in the heart by Katniss or Gale while they hide under some of Peeta's camouflage. Bella would run to him and weep and beg for death so she didn't have to live without him, and once she was dead, Edward would just slit his own throat or whatever it takes for him to die.
At least Peeta, Gale, and Katniss would be making an attempt to work together and stay alive.