At the same power, a person in the drops is going to go faster because they are more aerodynamic.

The point to notice is that if you sit up, you are generally capable of producing more power. This is why people sit up on climbs. The added available power is enough that you'll go faster, even with the added aerodynamic drag.

Since you seem to be interested. It's worth noting that in power on the flats goes up with velocity cubed, while power on hills goes up directly with velocity. This means that if you want to go twice as fast on a slow climb, you must produce twice as much power. If you want to go twice as fast on a flat road, you need to produce 8 times as much power.