Karin isn't a combatant so she loses by default. Her chakra chains are great, but I don't think she knows how to willingly pull them out to her will. She can heal wounds very quickly, but it can only be one person at a time. Karin is a sensor, so she would only be useful for scouting areas and finding enemies that are trying to hide. In this scenario, she is not very useful, unless Kakashi or Gai somehow ends up like Tsunade split in two and Karin comes to their aid to heal them, but most of that was done by Katsuyu and her stability with Tsunade's wounds.
Hinata pales in comparison to Sakura when it comes to overall attributes, such as being able to take out multiple enemies and heal an entire platoon at a given time. Hinata can't even heal, so she would already be at a disadvantage compared to Sakura. The seal that she uses when she killed those little Juubi is enough to say that she can help Kakashi and Gai when it comes to coverage.
Hinata's Byakugan isn't really going to help against opponents such as those, when she isn't nearly as proficient with it as Neji, so it's not going to be a huge asset to the team, but with Sakura, they can continuously heal with Katsuyu, or whatever her name is, and still be able to punch her opponents, while Kakashi and Gai handle the big guys.
Karin isn't going to be much help here, and Hinata is almost in the same boat as Karin.
Sakura has more resources and abilities at her disposal so she would give the team a better chance to win.