Similarity between Router and Filter is that both transformation would be able to discard data based on some filter condition.
The Differences are...
1.Using router transformation one would able to test incoming data for multiple filter condition and if none of the condition met the incoming rows gets rerouted to DAFAULT group.
2.Using filter transformation, one would be able to pass data to next transformation based on single filter pipeline condition. There is no option of routing data that doesnt match the condition like ROUTER Transformation.