If we are speaking technically, IM3 pretty much had more action in it than Avengers, which really only had 3 big sequences, if i would count the ones IM3 has it would be 5 major sequences and that's not counting all the action moments in between.
AVENGERS had 5 action sequences. Loki vs SHIELD,Cap/Iron Man vs Loki, the Cap/Thor/Iron Man battle,the battle on the Helicarier (which was divided into 4 separate fight sequences),and the long huge Avengers vs Loki and the Chitauri final battle scene.