The oxygen extraction efficiency of the human lung is about 25%. This of course changes in relationship to breathing rate, extraction efficiency drops with heavier breeding slightly. Given that air consists of a little more than 20% oxygen, we really do not change the oxygen content that much. Exhaled air contains about 15% oxygen. The main difference is the velocity that can be attained by fanning versus blowing. Since, within a confined space, you can often blow more air (or concentrate it) than you could lets say fan it (assuming we are talking your hand and not a big piece of fanning material), then the rate of delivery of O2 by mass/time is higher by blowing even if the O2 concentration is less.
Alternatively, I've been told that fanning an ember is more productive than blowing because the moisture on your breath weakens the flame. Here this argument would it seems holds water (HA HA HA HA....ROFL...LOL...HE HE HE HE, I'm killing myself here). The relative humidity of human breath approaches 100%. So in the tropics, breathing may make no difference at all since humidity is around 100% anyway, but in the desert - perhaps blowing could be less efficient.
I have no scientific data to back it up, but intuitively it would seem like moisture would more likely impact an ember because of the inherent weakness of the combustion reaction at that stage and might have less effect on an actual flame. Maybe a chemist or physicist can correct me on this one.