One thing that does impress me in the comparison of a G550 airframe vs 737-700 airframe is the rather spectacular stats of the G550.
G550 range: 12,500km (E-7A 7,040km, according to the RAAF website)
G550 operational altitude: 51,000ft (E-7A 41,000ft, according to the RAAF website)
G550 endurance: 14 hours (E-7A 10 hour mission*, according to the RAAF website. *Yes the E-7A has flown much longer missions, but of course that requires the aircraft to be aerial refuelled too).
What all that tells me is if you require an airframe to be able to travel very long distances, stay on station (without aerial refuelling) for a long time, and at a rather high operational altitude (G550 altitude is 10,000ft more than E-7A, it's on par with MQ-4C operational altitude), then the G550 appears to be the perfect solution....