While both split and window ACs have their own sets of benefits, the advantages of choosing the prior over the latter are:
Space: In window air conditioners, an entire appliance is a single unit. This means you have to designate a whole window to accommodate the AC. However, split systems come with an indoor and outdoor unit, which can be set up on either side of the wall. Thus, you get more flexibility with space requirements.
Noise: While the window systems can be a little loud, the split air conditioners are virtually noiseless. In air conditioners, the compressors are typically responsible for generating noise. Since the compressor in split systems is housed outside of the house, the disturbance is minimised.
Aesthetics: Because split systems can be suspended from the ceiling or hung on the wall, they blend better with room aesthetics when compared with window units.
Uniform cooling: The indoor unit of a split AC has a bigger, wider and powerful fan that throws the cool air in all directions and for longer distances. While a window AC has a smaller air-throw area, which makes space near the AC cooler and rest of the room remains at lower temperature.