Mounting the fan inside, outside, or half-in half-out will make no perceptable difference. What is important is how the air enters and exits the fan. The most efficient shape for air to enter a fan is with a bell-shaped inlet like those on
wind tunnels. Since very few people want to put a two foot intake on their case fan just to get a few percent increase in airflow, this isn't a common soloution. Air doesn't like to make sudden changes in direction or to have sudden expansions or contractions of space. When a fan blows into or out of a case, the air is suddenly going from a small cross-sectional area (the fan) to a large one (the case or room). This is not ideal for fan effiency. Fan makers try to help a (very) little by sloping the edges of the fan case out, but this probably has a negligable effect in real applications. If you were really serious about eeking out every last percent of effiency from your fan, you would put a cone on the front and back hubs (like you see on propeller aircraft), and ductwork to slowly change the cross-sectional area of the airflow, but again, with these size fans it's just not worth it.
Where you can really make a difference is by having a hole the same size as the fan (so there's no restriction or sudden change in diameter. Seal the gap between the fan and case. This keeps the airflow in a coherent direction into or out of the case without any "leakage". Mounting the fan half-in half-out would minimize air leakage, but the (maybe) .5% difference is just not worth the extra effort to cut, seal, and securely mount the fan. When I put in a fan, I usually cut a round hole and mount the fan with screws, using a washer as a spacer between the fan and case. I then put a bead of silicone between the fan and case, smoothing it along the inside of the fan with my finger. After it dries you can remove the screws. This helps keep the airflow smooth and insulates the case from the vibrations of the fan.