I just removed the last of the casement windows which were original to this 1966 house. Casements are great in the rain as nothing comes in but they do not catch winds crossing the house. They do catch wind going up, so for example, the smoking barbeque would set off the smoke alarm in the room with the window open.

It's personal choice which you prefer. Casement seem more contemporary, but you should be careful of doing things for fashion. Go and have a look at house which each type and make your decision.

I am sure that the last poster is referring to awnings, as casement open out to the side, not up from the bottom.

You don't necessarily get a breeze because a window "catches wind." You get a breeze because of a differential in air pressures causes air to move from one area to the other with the lower pressure.

We have both types in our new house and used awning in the kitchen and in the dining/living area -- it's open kitchen/dining/living. We have awnings high and awnings low. Thus, we get a cross-draft created with awnings on more than one side of the house open at once. Even a slight breeze outside gets "captured" so to speak.

And awnings are great in the rain too!

given the application (over sink) both sound about same in terms of air flow --- esp if there are other windows in the area to create the draw and differential pressures... They are just different from each other, especially in terms of the view out. That is where do you want and not want to see the frame? How large is the window opening? There are some casements that have no center vertical bar ... the two windows crank out to create one large unobstructed opening.
I have awnings at my sink in a rural cottage and that is perfect because it allows alot of open shelving above and (since we are not very tall folks) we can see out just fine. Sometimes they can be a little more difficult to crank tightly closed however. Where I have casements, I love them but am always conscience of not leaving them wide open lest it rain. Also depending on the height of the window above the sink, you want to consider which is easier to operate, in terms of reaching the hardware.

The house we lived in when I was in high school had awning windows. As previously mentioned they were nice because if it started raining (which happens a lot in S. FL) we didn't have to run around an close all the windows. My parents have since remodeled & have all casements which look more updated to me. Both will have the same airflow.