Aeroport consumes less box volume and you can get away with less port area for any given volume. Basically lowers overall box size and makes it easy to change tuning.
Slot port works great also (when done correctly) and is actually more versatile being that you can vary port length and area much more. A slot port also helps make the box stronger since it essentially functions as bracing too.
An aeroport box will usually outperform a slot port box if space is limited but when space isn't tight you can use way more port area with a slot port since they can be built longer (aeroport is limited to 18" without patching on additional tubing). Neither is superior for every situation, it all comes down to what will work best for a given scenario.
Hope that helps a bit.