Taxi or train, honestly
The train from Ben Gurion is good when it is running. The whole question is what happens when it is not, or when the last kilometre is the hard one.
When the train wins
Daytime, a station near both ends, one light case, and a timetable that fits. If all four are true, the train is cheaper and the taxi is not needed. We would rather say that than sell a ride that makes no sense.
When a taxi wins
A landing after the last train, a departure before the first one, Shabbat between Friday afternoon and nightfall on Saturday, three cases and two children, an address far from a station, or a meeting that cannot move. Those are the rides this service exists for.
The last mile
A station is not an address. The taxi's advantage is not speed on the open road, it is the fact that it ends where you are going, with the luggage already in the boot.
Questions
Does the train run on Shabbat?
No. Israel's trains stop for Shabbat. If your flight lands or leaves in that window, a pre-booked car is the realistic option.
Is the taxi cheaper than the train?
No, and it is not meant to be. It is faster door to door, it runs at hours the train does not, and it carries the luggage.