Both kinds of handlebars have advantages and disadvantages. I can tour comfortably with both including off road with a drop bar and long road tours with a flat bar (and bar ends). I have 2 touring bikes - each with the different bars. I switch bikes every few years when I visit my family in the USA where my bikes are stored. My thinking is that switching bike geometry and bar types gives my body a change that prevents overuse injuries. So the answer to what type of handlebar is better for touring may be to think of one have you been using the most and pick the other - or just pick the one you prefer - both do the job.

It is important that you have the right size bar. Drop bars come in different widths so the broader your shoulders the wider the bar. I am a big guy so I like a 44cm drop bar and my hands 44cm apart on a flat bar. Flat bars can be cut to the correct width. Whenever I build up a bike for a woman I usually cut the bars down some because their shoulders are not as wide.

Good travels to you!