Credit where it's due, War Arc Sakura and Prime Tsunade can probably beat Part 1 or even 1H Part 2 Hinata and Neji, but there is practically no way a fight between all of them at their prime can go in favour of team Tsunade.
And to those saying Sakura is Kage-level, she isn't. By the time of the Last, she's only Jounin-level. Neji was this by the start of Part 2, though granted Hinata was still Chunin as of the Last.
Finally, a theoretical fight should take into consideration the canonical implications of their abilities.
* Tsunade's CES is overhyped because of its effects on the ground -- look at the Sannin ruins fight for how it really damages when used in close combat (against Orochimaru). If you think being blown away is damaging, every female could already do that as genins in part 1.
* If their chakra gets shut town by gentle fist, neither Tsunade nor Sakura can recover themselves, however they should theoretically be able to heal each other enough, if given the chance, to allow Byakugou to heal them fully. Even THIS MUCH IS OVERRATED. During the Chunin exams, Hinata didn't recover from Neji's attacks FOR A FULL ARC INSPITE OF MEDICAL NINJUTSU from a GENIUS LIKE KABUTO. i.e. Medical Ninjutsu can't fully heal internal damages in the middle of a fight - it takes more time.
* CES do serious damage, though not 1-hit KO-like damage, if either Hyuga gets hit without defending.
* Neji and Hyashi have rotation, which can be scaled up and down to defend against stronger attacks. It also protects them in a sphere - ground-based attacks are no exception.
* Hinata also had an absolute defense, though it's NOT CANON, so leave it out.
Overall, for Hyuga to win, they need to hit Sakura and Tsunade with 64 palms in quick succession, before they can heal each other. They also need to avoid taking too many hits themselves -- easy for Neji and Hiashi, a challenge for Hinata. Chance of pulling off: 80%.
For Sakura and Tsunade to win, they need to actually land multiple clear hits on Neji and Hiashi. Chance of pulling off: 20%.
Note on Katsuyu: Her body is physically weak. Her main attack is a liquid acid spray, which < Rotation by a long shot. Neji can't beat Katsuyu, but Hiashi and Hinata can (Lion Fist).
Note also: Databook 4 gave them all elemental affinities. This makes these fights more complicated, and may, no doubt, tip the scales in team Tsunade's favour. and that's a big MAY.