I would say if you're trying to get back to the beach after losing a board, and you're like the rest of us on the east coast where you are basically going back in through a heavy beach-break, your best bet will be either breast stroke or side stroke. One advantage of side stroke is you can actually see what's coming down on you from behind, keep your head out of the water for constant breathing, and make fairly good progress if your side-stroke kick technique is pretty good.
Keep in mind that efficiency in swimming comes from control over your rhythm and timing, especially your breath timing. You will quickly become exhausted no matter how in-shape you are if you start flailing in the water and gasping for air. Whatever stroke you choose, you want strong, deliberate (not rushed) strokes, and as controlled and consistent a breathing rhythm as possible. I often personally like to count my strokes to make sure they are happening to a consistent beat. You do not want to constantly find yourself having to accelerate/decelerate in the water ... THAT will wear you out very quickly.
It's these criteria that make me believe that in heavier surf, freestyle is a poor choice. Efficient freestyle is all about relaxing and gliding through the water, but none of that is going to be possible in heavy surf. Additionally any breathing rhythm you may attempt to maintain will be shot each time you tilt you head and get a mouthful of water. In order to avoid that, you're going to have to over-rotate to really get your head to the side or even out of the water, but at that point, you're actually in the correct position for side-stroke, and in very bad form for freestyle.
While freestyle is definitely much faster than any other stroke in ideal conditions, when the surf gets big and the water is rough, you're going to lose a lot of the efficiency that normally makes freestyle fast. In order to maintain the ideal scenario of consistent rhythm with strong, smooth strokes, a swimming style such as side-stroke or breast-stroke will most likely be the best bet, even if it's not the fastest way back to the beach.