1996 Mercury Sable catalytic convertor or O2 sensor?

Engine Performance problem
1996 Mercury Sable 6 cyl Front Wheel Drive Automatic

i have a 96 mercury sable v6 12v, my question, is the engine light is on and the mechanic said it show o2 sensor, but another mechanic said it could also be the catalytic convertor. U can have plenty of gas n the car but sometimes it feels like it is out of gas, because it will lug way down and jerk, the car never dies, but u have to kill the engine wait a few minutes and restart then it will be fine, and other times u have to kill the engine every other mile or 2, so could this be a fauly o2 sensor or a cat? When the air conditioner is on it chuggs really bad, and my kids say they smell gas when they r in the back seat, it reads off o2 sensors not cat sensors. Thank you for ur time.