Oh jeez, did you just re-open one of the perennial cans of worms.
The answer is, “it depends on your intended usage”. The ballast box can do more for directly offsetting weight in the loader, with less weight in the box than the tires, since it’s further aft. If you don’t understand that, google “leverage”. Also, a ballast box is removable and reconfigurable, whereas loaded tires are not.
More importantly, any ballast put on your 3-point, whether ballast box or other, take load OFF of your front axle. In some cases, the capacity limits of a given loader on a given tractor may even depend on this. Loaded tires do nothing to reduce stress on the front axle.
The advantage of loaded tires is that they’re lower to the ground, and offer better side/side stability than a ballast box ever can. It’s also easy to carry more weight in the tires, without creating the bucking bronco effect of having all your ballast fore and aft of the axles.
The solution for most is a combination of the two. I have my tires loaded, but I also have a ballast box, and I also welded carriers onto that ballast box to carry an additional 17 suitcase weights. Between these three forms of ballast, I can configure the tractor for any task. When doing light lawn chores, the ballast box is left in the barn, and I’m only running my loaded tires. For moderate loader work, I add the ballast box. If I’m lifting something that’s really putting the tractor at its limits, then I start adding the suitcase weights to the ballast box.