Smoothing cap vs filter for full wave bridge rectifier circuit
Using an LC filter reduces the demands on the transformer and capacitors. Ripple current in the capacitor is reduced, peak and RMS diode currents are reduced and output ripple voltage is less for a given value of filter capacitor. 

A 10A rated transformer with an LC (aka 'choke input') filter can provide 9.4A of DC vs. 6.2A with just a filter capacitor. 

The downside is that, particularly at mains frequency, the choke (inductor) is large, heavy and expensive, more so than just buying a bigger transformer, if it is high enough value to maintain constant current during the cycle. For that reason, it's seldom seen these days.