The advantage of curley/drop bars over flat ones is in the variety of positions available and the neutral wrist set of the usual (top of the brake lever) position.
Flat bars put a bend in your wrist which concentrates the vibration. Bar ends are spaced to far apart, and produce a parachute effect with your arms. You can use aero bar extensions on flat bars and they are more efficient and more comfortable than bar ends.
How high/low near/far your drop bars are is entirely a personal choice. Although most production bikes with drop bars assume a sporty position, many tourists using customised bikes have their drops set higher and closer.
You can use drop bars with fat tyres. Thorn bikes at sjscycles.com make an interesting range of touring bikes using MTB wheels and drop bars.

You can get drop bars in different shapes, widths and drop radii. Tourists often prefer small radius drops, with extra curves, like the 3ttt morphe.

These days, drop bars are hard to market, so the shops are full of touring-style bikes with flat bars.