The war arc is one instance where Naruto has fought multiple opponents. Before that we need to look at their fights closely.
In part one they both fought Zabuza and Haku.
They both had the same amount of fights in the chuunin exams barring Orochimaru. And Naruto actually had three complete fights with Kiba, Neji, and then Gaara whereas Sasuke only fought that chakra freak and had his fight with Gaara interrupted.
Beyond that Naruto had fought Kabuto along with the sannin and then fought Sasuke twice while on the rooftop and then later at the valley of the end.
In part 2 Sasuke had defeated a multitude of ninja and then subsequently fought Deidara. He then fought Itachi, Killer Bee, the Hokages, and Danzo and Kabuto.
Naruto had a scuffle with deidara but no real fight, and then he had his skirmish with Kakuzu. I don't necessarily call that fights, but Kakuzu was certainly an experience. Naruto then fought Pain, Edo third Raikage and then the edo jinchuuriki.
Technically Naruto has had more altercations than Sasuke considering part 1 and part 2 combined, but it seems that Sasuke has had one more complete fight than Naruto.
It's about even to be quite honest with you
Sorry if that was long or I missed something
Oh and I think Naruto fought himself in that dark waterfall place and then the kyuubi. And Sasuke also fought Orochimaru.
edit: Sasuke also fought Itachi in part 1... Or got his ass kicked. Still an combat moment regardless
