it definately has to do with the engines, since the VF-0's engines are so fuel-hungry, the VF-0 needs to hold enough fuel for it to go fight for like 30 min with a 2 hour loiter time (somewhere near that long) and still make it back to the carrier. since the VF-1 uses Hydrogen for fuel, all it has to do is just fly and suck the air to get it's fuel, so it can fly as long as the pilot basically wants to, needing only a small space to store fuel.
as to the advantage for size, usually the smaller the aircraft, the more manuverable it is, hence, the VF-1 being able to outmanuver the VF-0 (be cool to see a VF-0 vs a -1 dogfight, to see how unbalanced they are)