I learned to ride on the drops because the hills in my complex have steepness grades ranging from 4% to 40% (per Google Earth). I was new at biking and didn't want to go down hill more than 10 miles per hour. The only way to brake slow enough was for me to use the drops (you can squeeze the brakes stronger on the drops than on the hoods). So, I was forced to use the drops and now I feel that I have much better braking control.

Also, I learned that going downhill, your feet should be even (at 3:00 and 9:00) for better balance and that you use your thighs to squeeze the saddle for better control if the bike shimmies/wobbles. You can also move your buttock a little bit more towards the rear of the saddle when you ride downhill on the drops.

I'm a newbie, so take my advice with a "grain of salt". Now I go probably 40mph (which scares the crap out of me still) as I scan the road for objects that can flip my bike over and for cars.
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2012 Specialized Amira Elite, upgraded carbon handle bars, Jett saddle 143mm switched to 145mm 2012 Selle Italia Max SLR Gel Flow saddle

2011 Specialized Ariel Sport,suspension post,Serfas Rx Women's Microfiber saddle