Ease of transfer (one pilot vs multiple for a looooong flight, probably no refuel on the Antonow, and if so it eats less specialised stuff than the F-16s) and maybe even fuel efficiency, I would guess.
Also, one cargo plane raises less eye brows than a flock of fighters.
The maximum range for the F16 in "ferry" mode (max fuel, no weapons, pee before takeoff) is something like 4000km. The distance from Belfast (Maine) to Belfast (the original) is 4500km.
That would mean air to air refueling, which is expensive and risky. It would put major wear on the planes, which are not the newest to start with. And unlike the Antonov, the F16 comes with neither legroom nor bathrooms.
Iirc the factor that limited early nuclear submarines the most from continuous dives was the toilets, they have limited storage for sewage and it turns out that draining those with a greater outside pressure is a pretty difficult task, at least if you want to stay undetected.
Now that they have figured that out the limiting factor is food.
There's no way it can get anywhere near that range at full speed. Fighters need to use afterburners to get up to max speed, and F16s run out of fuel in about 10 minutes when using afterburner.