Wheel size is a hotly debated topic in both the street-custom and racing scenes. Within the confines of stock upgrades, few issues are so contentious as "upgrading" from stock 15-inch wheels to 16-inch models, and for good reason.
Assuming that the tires used have the same diameter, 16-inch rims will shorten the distance from rim to tread, reducing the tyre's sidewall height relative to its width (aspect ratio).
Reducing aspect ratio decreases the tyre's propensity for flexing under hard cornering and is a well-known method to sharpen handling. Sixteen-inch rims are often offered as factory options for just this reason.
Because 16-inch rims are largely obsolete, tire selection is very poor. This is the single biggest argument for 15-inch rims; it is very easy to find anything from off-road mud tires to road-racing slicks that fit.
If there is one good reason for 16-inch tires, it's that they may provide extra clearance for those who wish to run larger and more powerful brakes.
Modern 17-inch rims will provide the brake clearance and handling of 16s, but are almost as well supported by tire manufacturers as 15s.