Best style of window for above grade basement windows?
Honestly, letting your wife pick what looks best is the answer.  The double tilt sliders are nice if you want to pop them out and clean them I guess. I like the awning ones because you have a bigger window area without sashes in the way.  If you do get the awning style, make sure the crank mechanisms are replaceable.  I have one in my bathroom that basically isn't repairable without taking the whole thing out. Whether you will actually be opening and closing them and how much airflow you want to have is another consideration. You may not want to have to crank it in an out or remove the screen to unlock it.