I have one of each.
Well the first bike used to have a flat bar but now it has a trekking/butterfly bar for greater variety of hand positions.
The drop bar is on an adventure road bike. The saddle, handlebar, etc. are all set up so that I can ride it with a slight forward lean. While my torso isn't perfectly upright, it's close enough that I have no trouble swiveling my head around to observe traffic - and I don't have any special neck flexibility either. That is why the type of frame on this bike is called "relaxed geometry". The one that the the OP is talking about is an aggressive geometry bike, where you're leaning a lot more forward for that racing posture. The LBS of course made sure I got a bike with an appropriately sized frame then put me through a basic fitting session.
If you have a road bike and you're really hunched over, your frame could be too aggressive for your tastes, or you have the wrong size of bike, or you haven't been fitted properly to your bike.
Last edited by GovernorSilver; 02-21-16 at 03:22 PM.