How do you compare private jet and commercial jet efficiency?
This has nothing to do with private vs. commercial. The size difference is what matters.

If you compare the absolute cost of moving the aircraft from NYC to LA, the 737 will be way more expensive, regardless of version. Since you asked only which one is more expensive, I don't see a need for detailed reasoning. Just use the data provided in this answer and it becomes obvious that fuel consumption will scale with the mass of the aircraft.

If all passengers have to share the cost, the cost per passenger will be much higher in case of the Phenom 300. Or almost any other Bizjet. The Phenom will even need to land somewhere enroute to refuel. The distance from NYC to LA is bigger than the maximum range with full payload.

But that kind of comparison does not make sense - both airplanes have been designed for different purposes, so their strengths are in their unique field of use. They do not transfer well to that of different aircraft types.