The Beer Box actually looks pretty good for what I do.
I brew about 10L batches, so I can fit a whole batch in each of the two beer boxes you get with one order. With tap-a-draft I would have to order an extra 6L bottle to be able to do two full batches (you only get three bottles with an order), which adds $10 to the price.
With tap a draft it also looks like I would have to order an extra valve (at $45) to be able to dispense beer from two different bottles at once, whereas with the beer box each box has its own tap (the co2 cartridge is only used to maintain pressure in the box so you can dispense the beer, so it can be moved from box to box when they're running low).
Also, the tap a draft system recommends that you replace the bottles every ten uses, which is an additional $40 cost (+shipping) every so often (if you google it, you'll find stories of peoples' tap a draft bottles spontaneously breaking in their fridge and getting beer everywhere, so I wouldn't want to push it by using the bottles past the recommended ten uses). The beer box is made of a much thicker plastic and looks like it would last significantly longer than ten uses.
Finally, the beer box is (roughly) a rectangle, so it should take up less overall space in my fridge for the same amount of beer (although the tap a draft system has the advantage of the fact that, when you've used up one 6L bottle, you can take it out of the fridge to free up space; the beer box has to stay until the whole thing is done).
One advantage of the tap a draft system is that the plastic is somewhat see-through, meaning that I can see how much beer I have left with a glance (with the beer box I guess you have to pick it up and try to guess how much you have left by weight...not the most convenient). I suppose you could argue that the reduced light permeability for the beer box is a plus from a beer quality standpoint, but given that it's going to be in a dark fridge for 99% of the time it probably doesn't really matter.
Anyway, other than price, I don't really see any significant advantage to the tap a draft system. And even with price, when you add on the money for the extra bottle, the extra valve, and the replacement bottles every 10 uses, it doesn't look like such a good deal after all.
I haven't ordered anything yet, but I think I'm going to get a beer box. The extra money up front seems worth it in the long run for me.