Together with the University of Florida, the Earthbox company ran a large scale side by side test that you can see here (pdf). I think it's important to question the validity of the study, who did it, what assumptions were made, etc. But to dismiss it simply because "they're selling a product" seems like the easy way out.
Without numbers, it's harder to persuade some people. What we do have is our experience. We're happy with it, but would like to improve on it.
We used the earthbox idea as a basic platform for several reasons.
We wanted something that was human in scale, easy to explain to non-gardeners and still produced better results using fewer inputs than was possible on the ground.
Because we're on top of roofs, weight is an issue.
We wanted to be able to reproduce our "concept" using commonly available materials. If it was too difficult to make or to operate, we changed it.
We've only done this one year, though the earthbox was invented in the early 90's. I don't know the history, but I'd guess that there are plenty of people who have more experience using better systems, it's just that we couldn't find them.
I don't think they've found a renewable source for peat, though if you've got one I trust that you'll pass it on.
I'm not, by any means, dismissing the idea out of hand, I'm just not impressed by the sales spiel. In fact, the idea of covering hectares of land in little plastic boxes seems somewhat crazy to me: this criticism obviously doesn't apply to growing food where there isn't any available land. I'm just asking questions to learn why choices were made and to see if there's anything useful I can offer.
As I said, I've found that smaller containers require far too much work to make them successful, especially when they're relatively exposed to the elements. I'd say that even on the south facing Irish patio that we had in the last house the container size you have is barely large enough. Larger containers, with multiple crops in them, seem more stable under temperature changes and hold water better. They also form a more viable soil eco-system. I'd be inclined to experiment with 2x4 or 4x4 wooden containers 8" deep with buried reservoirs if I was doing what you're doing.
The issue of appearance may or may not be important: it depends on whether you want the space to be useful as a garden as well as a food production system. My inclination is to make the space somewhere you want to spend time - the best fertiliser is the gardener's shadow and all that.
Sometimes you get the same answer when you ask "What setting lets us use this?" and "What would we use for this setting?" ... oftimes, though, you get different answers. Utsukushikereba sore de ii
They tend to be sold at a premium, though the size of this varies (without any obvious cause beyond the price-insensitivity of conscientious objectors) between the minimal and the substantial.
However, since the introduction of our three-bin system (recycling, garden and general waste), the local recycling centre has been selling compost made on its premises-and at a really good price, too.
In terms of a slightly more sustainable peat source, some "mushroom composts"-the spent growing medium from commercial mushroom farms-contain peat. Not ideal, but at least it's recycled.