I'd go with the 7800 but I'm not sure which games were available in 1986. Many games have 1987 copyright dates but I don't know if they're accurate or not.
With that in mind I'd go with the NES since I'm not sure if I can choose the 7800 according to the rules of the question:
Balloon Fight
Pinball
Kung Fu
Popeye
HOWEVER, assuming some of those 1987 release dates must be wrong unless there were no 7800 games when the system was released (would seem stupid, even Pole Position II, the pack in game has a 1987 copyright date) I'd go with the 7800 and
Food Fight
Ms Pacman
Galaga
Centipede