What are the advantages of full wave bridge rectifier with capacitors parallel to diodes?
Power supply transformers have leakage inductance and parasitic capacitance, and when the diodes in a bridge rectifier switch off these "non-ideal" elements form a resonant circuit that can oscillate at high frequency.  This high frequency oscillation can then couple into the rest of the circuitry.  Snubber circuits are used in an attempt to mitigate this problem.  Just using capacitors doesn't damp the ringing completely, but does cause it to drop to a lower frequency where the coupling effect is less.  An RC circuit across the diodes can damp the ringing almost completely.

You can read more in the following excellent paper:
http://www.hagtech.com/pdf/snubber.pdf