I looked into getting a 360 and probably wil, but since it's inside a garage I figure let him store it until I'm ready to take on another bike.
The plus is that it is a six speed.
The difference is that the pistons on the 350f hit TDC simultaneous, and valve and spark determine which is firing (lost spark system). The 360 is on TDC alternating between pistons at TDC. The 350 has a tubular fame, the 360 is unitized, and some say not as stiff.
The 360 does not get as good gas mileage.
By the time the 360 twin was out eveybody was tuning their 350's so there are many after market upgrades, the 360 not so. Everyone just kept to what they had, the 350's, instead of buying into the more engineered 360.
But if for your purpose, a bike for your wife to ride it could be good. It has the right styling compared to a ninja 250 if you are riding together. There are a fair number of parts out there for the 360.