Window air conditioners will often limit the way you use your window. Even when you want to let in even more light or fresh air, the window conditioner gets in the way. Wall mounted air conditioners do not bring such issues.
Second, compared to window air conditioners that can be easily reached by burglars, wall mounted air conditioners can be installed virtually anywhere you deem fit which means that burglars will not get to them easily.
Saving space is another benefit with wall mounted air conditioners. Compared to standing or cabinet air conditioners, which will need their own space, wall mounted air conditioners can be installed up on the wall where they will not get in the way.
However, wall mounted air conditioners do come with their own set of cons. Firstly the units are normally not powerful enough to cool the entire house and are often only effective in single rooms.
Installing the wall mounted air conditioner is a bit more expensive than with the window AC. It needs access to outside air which means you will have to drill a hole through the wall.