Actually, the Saturn V is the largest rocket ever successfully launched. See: Falcon Heavy vs. the classic Saturn V
Leaving aside minutiae like specific impulse and burn times, what does all this mean at the end of the day? It means that the Falcon Heavy can put a payload of 140,700 lb (63,800 kg) into low Earth orbit at an inclination of 28.5 degrees. It could also reach escape velocity to send 35,000 lb (16,000 kg) to the Moon.
Saturn V? Its low Earth orbit throw weight is over twice the Heavy's at 310,000 lb (140,000 kg) with a 30° inclination. Getting to escape velocity, it can loft 107,100 lb (48,600 kg) into lunar orbit...
But where the Falcon Heavy comes out ahead is in economy. The estimated cost of a Saturn V launch in today's dollars is a whopping US$1.16 billion. Meanwhile, the upper estimate for Falcon heavy is US$90 million. That's million with an "M."