I use both, it just depends on the situation.
A 48" box blade is going to weight anywhere from 275# to about 400# depending on how light or heavy the construction of the blade you choose. Obviously a light duty box blade is not going be nearly as effective at adding stability as a heavy duty blade. As was already pointed out, a
ballast box is a lot more compact than a box blade. If you are working in tight spaces, around your buildings, fences, or trees, then a ballast box may be a better choice for your ballasting needs.
I also use my ballast box to carry tools and other things. If you take a couple 4" diameter PVC pipes and insert them vertically into your ballast box, then pour sand or concrete around those tubes, you can then insert long handled tools into the PVC pipes and use the ballast box to carry the tools vertically out to your worksite, while only giving up a little bit of weight of the ballast box. Tools can also be strapped/bungied to a box blade, but generally you lay them down which makes them stick out even farther, therefore harder to maneuver in tight spaces. If you don't have tight spaces, then no problem!
BTW, if you weld or bolt some heavy duty casters onto the bottom of your ballast box you won't regret it!