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LC-type filter will provide more attenuation but L's are usually more costly and they take up more board space. Plus, inductor cannot be integrated well. You get 20dB/decade attenuation per reactive element. These filters are usually passive (they are used by themselves, without opamps).
RC filters have lower attenuation but can be integrated much better and are more flexible. RC filter are usually used with opamps to form what is known as active filters.