Bottom-Feed (aka siphon-feed) airbrushes allow the user to change colors quickly and easily. They can also carry a lot of paint when a large bottle is attached. These work great for T-shirts, murals, temporary tattoos etc. Some artists who have developed their airbrush skills through painting T-shirts professionally, go on to use the bottle-feed style in other applications because they get so used to the feel of it and its color changing system. To each his own!
Side-Feed airbrushes are similar to bottom-feed except that the paint cup or bottle is attached to the side of the airbrush rather than the bottom. A major advantage side-feed airbrushes have is that the paint reservoir can be rotated. This allows the airbrush to be sprayed at any angle; including upside down. This design is great for projects that may require painting in odd positions such as ceilings, auto interiors or motorcycles. Some illustrators, modelers and others also like a side-feed airbrush because it does not block their line of vision the way a gravity-feed airbrush can.