I think the tops/drops benefit is more based upon the position of your back than your hands. Personally, I prefer to get low but with my hands on the STI. But, I must do some more riding on the drops and see if it makes me any faster.
My direct experience - I used to have a perfectly flat commute and my "normal" speed for knobblies was 14mph. This was borne out by the global average of 1500 miles in just over 100 hours. I fitted 26x1.5 slicks from the supermarket and it added 2 to 3 mph for the same effort.