Is the goal of either airline to make it much more attractive to travel on the other? They're not sharing revenue so neither of them really wants to drive traffic to the other for their elites.

I think the cross FF benefits are mainly to dress up a slot swap that is arguably anticompetitive - the airlines can tout the benefits to customers as a justification even though this arguably solidifies United's entrenchment in the NYC market and helps prevent others entering or expanding (i.e., through Jet Blue's JFK slots).