According to the ועד לעניני תחבורה the main criteria is whether or not the flight has movies shown. They split up the airlines into 3 groups.
Preferred - no movies shown
Second choice - movies but only on a personal screen which can be shut off
Third Choice - movies on a main screen
On the Tel Aviv - NY route for example, there are no Preferred airlines. Continental and British are second choice and El Al is third choice (because they have some planes without personal screens and the movies they do show are particularly bad (according to the Vaad). I wonder how they know this? Who watched the movies for them and compared?).
For some reason, they left out some popular airlines on the Tel Aviv - NY route. I know from personal experience that Lufthansa is very popular. They would probably be a third choice because on their trans-atlantic flights they have a lot of planes with movies on the main screen. They also left out Delta which has a non-stop flight Tel Aviv - NY as well as Tel Aviv - Atlanta.
Interestingly enough, Arkia and Israir are prohibited completely.
You can see the whole list below: