Although both a rear blade and a box blade can be used for leveling ground, there is a big difference in how they do it.
They both excel at certain tasks, but can be awful for other tasks. For instance, a rear blade does a reasonable job with snow -- mostly backward, but for snows up to 6 or 8 inches, it is usable in the forward position. A box blade isn't good for more than just a few inches of snow.
A rear blade just pulls dirt. On most tractors, it can be angled and positioned a lot differently than a box blade. Much of the dirt that is accumulated in front of the blade slips past one end or the other of the blade. Certainly some dirt slips under the low spots of the blade.
A box blade is just that. It is a box with grader blades. One grader blade faces forward. It scrapes. The other blade faces backward. It is used for smoothing or filling if you are pushing backward. Very little dirt escapes from either side, so a lot more is available for filling pot holes and ruts.
It also has "scarafiers" in front of the front blade. These are real nasty heavy duty teeth that can be set to dig into the ground in front of the scraper blade to loosen the earth. These teeth can be adjusted to dig deep, or to never touch the ground. You can move and level a lot of ground with a box blade.
On most tractors, there is no down pressure on the 3-point hitch. Down pressure is determined by the weight of the implement. This isn't exact, but a rear blade usually weighs about half what the same width box blade weighs.
I do most of my driveway grooming with a rear blade. But, come spring time after pushing a lot of snow (and gravel) off the road, or after very heavy rains, the box blade gets put to work pulling the gravel back to the road, filling in the ruts, and cleaning out the ditches.
For your use, it sure sounds like a box blade would do a lot more for you than a rear blade.