Both airports are 50 miles from each other. Any private transfer will almost certainly get relatively expensive. Narita airport indicates that the fixed taxi fare to the Haneda is ~22,000¥ + highway tolls.

Personally I would take the Limousine bus. It's only 3,100¥/person, is probably just as quick as a taxi or other road based transfer and has the advantage of avoiding going through Tokyo on the train.