I'd put it this way. Do you need an airplane to get to the hardware store across the street?
This questions your goal. Both filters are VERY capable biologically, and may be a significant overkill for the majority of real life home tanks. So, do you really NEED that much of capacity (considering the cost, maintenance headaches, noise/evaporation issues of W/D, etc.)? They are not "turn it on and forget" filters. In fact, they're very far from it. You're not going to be comfortable during your vacation in Paris knowing that your tank at home depends on one of those.
Now, you cannot compare capacities based on the word "large".
If you compare the same volumes of biomedia, sand will be more potent (the total surface area is MUCH higher, so, even if the media oxygenation is lower, the huge difference in the total surface area would win the game). However, if you insist, I'd guess that the largest Amiracle filled with Mini Bioballs will be equally or, most likely, less potent than, let's say, LF 300 (which is not the largest FBF, of course). I'm talking about nitrification capacity only.
If you want my personal opinion, I hate FBFs (I had major headaches with LF300 and would never try it again). As for the sump-based W/Ds, I'm not too fond of them either (I run one now and would hardly want to build another one). There are better options for any of my tanks.