There are many advantages, but the most obvious to me
Advantage 1 :
Oversampling followed by decimation allows you use to simpler and smaller anti-aliasing filters. These filters cost less and take up less space on a PCboard.
Advantage 2 :
In multi-channels application, the tolerance and variation of the analog components of your anti-aliasing filters can cause skew between the channels because of the analog bandwidth tolerance. The cut-off frequency is determined by the value of the resistors and capacitors. While it's easy to get resistor with a ± 0.1% tolerance, it is much harder to get capacitors with a ± 0.1% tolerance. A ballpark estimate yields a ± 1% bandwidth tolerance for an order-1 filter, 2% for an order-2 filter, etc.
Oversampling followed by decimation will make the overall bandwidth more dependant on the digital anti-aliasing filter (in the decimation process) and less on the analog anti-aliasing filter. If your application requires a 0.1 % bandwidth tolerance between multiple channels, oversampling is the way to go.
You need faster ADCs and faster digital electronics (CPU, or FPGA). It costs more and usually draws more power.