This is essentially due to a difference in the speed of the airflow in each case. When we breathe out slowly on our hands, the warmth and moisture from our mouths has time to transfer to our hands, warming them up. But pursing our lips speeds up the airflow, and as this passes over our hands, it blasts away any air that’s been warmed by contact with our hands, cooling them. In addition, the fast-moving column of air draws in, or ‘entrains’, the air around it. This tends to be cooler than our breath, so it boosts the cooling effect.