My thoughts on this... Based on my 10-15 years of competitive swimming (though I sucked), and quite some time spent swimming later on.
First, you'll need to define efficiency... Are you looking at liters per minute, liters per meter? You might not even do the same dive.
Flutter is likely faster. Depending on the person. At least, when there's no gear on.
When there's resistance to fight against, in my experience, you're better off with frog kick. Some background on this. When I trained for swimming, there was that big guy that would simply destroy me on any race (but we weren't in same category). At some point in the training, we did some "band training", with a rubber band pulling us towards one end of the pool, and we had to stay as far and as long as possible from the side.
On the first try, everyone but me went for freestyle, because to me it seemed obvious to go with the technique I mastered, which was breast stroke. Well, I was the one that went the farthest and longest. Then, the trainer suggested to others to not use freestyle... and everybody got farther than he did on his first try (except me).
So yeah, to me, if you're pulling something heavy, you're better off not using flutter kicks.
But at the end of the day, I hardly ever had a dive I considered exhausting and/or too short, so I'm really not worried about this whole SAC thing.