In my experience, the bulk of linear AC-DC power supplies only use a capacitor after the diode bridge. There are probably a couple of reasons for that.
First, pros for LC:
An LC filter will give you a more tightly regulated output voltage, which might be important if you are not planning on using a regulator. It also lets you get away with using a smaller capacitor (than would be required for similar performance in a capacitor-only filter). That might be important if you are designing a very high current supply.
Cons for LC:
There is a voltage drop across the series inductor so your average voltage will be less. This may or may not be an issue. Probably the biggest con is that they are expensive and bulky. In general, engineers try to deal with inductors as little as possible.
I'd say for relatively low currents and when you are using a voltage regulator, like you likely are, a capacitor filter is generally good enough. As long as your minimum voltage across the filter capacitor is greater than your maximum desired output voltage + drop-out voltage of the regulator, you are covered.