Both implements will follow the terrain if you float the 3-pt hitch and let the implements ride on the ground. And both can create irregularities out of phase with the front wheel if the 3-pt is holding them up, to the point of whatever downforce the implement creates. What I mean by that is that if your front wheels hit a bump, the rear blade (either one) will dig down and make a dip. If your front wheels go into a dip, the rear blade rises up and will deposit any material as a new bump. It doesn't take much of this before you turn a minimally bumpy road into a more bumpy road. So I almost always float my box blade and my rear blade unless I have a reason not to.
The main difference is that the rear blade is capable of moving material laterally when angled, for instance from side to crown. The box will not. The box, however, is great at redistributing material as it collects in the box. It will shave off material from high spots and fill in low spots. A box is great for distributing gravel (even coarse gravel like #3) or smoothing dry topsoil (damp topsoil tends to clump and stick; if that happens I go do something else for a couple hours while the sunlight drys out the soil a little).
A box is a lot more rugged than a rear blade, though there are HD rear blades that are pretty stout. But still, the construction of the box makes it like a bulldozer of sorts.
The only time I have had occasion to angle my box side to side is when cutting a ditch. A reinforced rear blade with offset and angle would be the best tool for that, but a box will do. But otherwise, I almost always have my box level side to side for grading, smoothing, and moving material.
I had some deep logging ruts on my property, left by skidders when the land was logged in the early 90s. In fact, the ruts are visible on google earth in some shots! We had to cross one set for our driveway, and all I did was fill them in with #3 gravel before compacting and topping with road base. In another area, I used the box blade to shave off about 12" of loamy topsoil before putting down #3 then road base, and it worked very well for that.
Where the box isn't so great is when there is a lot of debris in the soil (roots, sticks, rocks, etc). It ends up getting caught in the box and disrupts the smoothing/cutting action of the cutting edges. You will periodically need to stop and empty the box, then push the debris off to the side.
You may be able to yank out roots with the box blade rippers, but don't be surprised if you run out of traction or grunt, even on a heavy tractor. They can be like arresting hooks in some cases. Running a box blade with rippers down is as intense as tilling, without the benefit of rotating machinery. I could bring my old tractor to a standstill with rippers down in heavy clay soil or soil with a lot of roots, by loss of traction. My new tractor runs out of steam before it runs out of traction in the same conditions. Where the rippers work well is in clear soil or gravel.
The biggest trick for grading with a box blade is adjusting the angle of attack with the hydraulic top link, especially for boxes with dual forward and rear cutting edges. It lets you tune the angle of attack for both cutting edges. This gives the ability to dig or smooth, in forward or reverse (though note the 3-pt arms are not made for excessive pushing in reverse, so I generally limit reverse work to smoothing only).
Going forward, lengthening the top link makes the box less aggressive at digging and better for smoothing, as the front cutter rises up and the rear cutter feathers (in the limit when the front cutter is off the ground and the rear cutter is fully feathered, it provides very gentle smoothing). The opposite happens when you decrease the top link length -- the front cutter will bite more and more. Opposite action when going in reverse.
