A new track has been put into use not too long ago, reducing the total travel time from four hours and nine minutes to three hours and eighteen minutes. When flying the skies it becomes a bit more difficult to estimate total traveling time. Let's assume a check-in takes about one hour, a flight thirty minutes and checking out no more than thirty minutes. That leaves us with with two hours. However, since airports are mostly located outside the city centre (they are in Amsterdam and Paris) it is fair to add at least another hour for traveling from and to the airport. These times could differ in practice due to various causes, but the estimates are quite close so I call a draw. Flying will take you three hours.
Next thing to check was the cost for a ticket. These prizes vary depending on when you book, but the train was mostly cheaper at around €55,- for a return ticket. A plane ticket would cost you no more than €90,- including taxes.
Last but not least, CO2 emissions. Not surprisingly, the train wins big time here. It produces around 26 kg CO2 per passenger compared to 50 kg pp on the plane. Of course these estimates depend on how well the train and plane are filled and so could vary slightly.
Decisive results I think. Other advantages of traveling by train: cell phones allowed, internet available, more room/comfort, more seats available on shorter notice. So next time you're visiting Paris (or Amsterdam), travel by train!