I ride the drops whenever I am going downhill... adds some stability... and I also "squeeze" the top tube with my legs for added stability... if I want to ride a downhill slower, I will moce my hands to the hoods and the wind hitting my body helps decrease my speed...

riding in the drops is definitely more aerodynamic and prevents you from becoming a "sail"... if you watch racers they ride almost exclusively in the drops EXCEPT when climbing... it is recommended to ride on top of the bars then, to allow better air intake into your lungs...