Using two tomato hanging bags, I planted a "Better Boy" tomato plant in one and a "Sweet 100" tomato plant in the other. I also planted the same two varieties, purchased from the same tray in the same store, in a raised bed. The primary difference in the beginning was that the hanging bags were filled with a name brand potting soil that contained some balanced fertilizer, while the raised bed was filled with soil amended with compost and no fertilizer.
It was noticeable right away that the hanging plants grew faster, but not bigger than the ones in the raised bed. By the end of the season, the plants in the ground were bigger, bushier, stronger, and bore more fruit.
The hanging plants flowered and set fruit, but in dramatically smaller numbers. For the "Sweet 100" plants (a cherry tomato) I harvested nine tomatoes from the hanging plant and more than sixty from the plant in the ground (there were many more unripe tomatoes on that vine when the first frost hit). For the "Better Boy" plants I harvested four tomatoes from the hanging plant and about 20 from the plant in ground (it too had many more unripe fruits that were affected by the frost).
The obvious conclusion is that tomato plants in a raised bed will produce much more fruit than ones grown upside down in a bag. I didn't notice any difference in taste.
Topsy Turvy, the one you see advertised so much, guarantees 50 pounds of tomatoes from their Tomato Tree set that holds multiple plants. That averages out to a little more than 12 pounds of tomatoes per plant, not a lot. If you look closely at their advertising photos you can see that the individual plants only have a dozen or so tomatoes on them when fully grown. I'm used to more than that on my garden plants.
Online reviews from many of the customers of these systems seem to show similar results to those I had. If you plant upside down and expect abundant fruit, you'll probably be disappointed. However if you plant upside down on a deck or patio because you don't have garden beds, then it gives you the chance for tomatoes that you wouldn't have otherwise.
I've tried to analyze the results and have a few conclusions. Though the claims are that the system uses gravity to draw nutrients into the vine and fruit and make them bigger and better while it allows roots to grow up, this is counter to the natural way plants grow. The tomato vines in my upside down planter were still trying to grow "up", using extra energy and distorting the vine, while the roots also tended to grow "down" and not expanding well within the container; this led to fewer flowers and less fruit.
The weight of the fruit put them low while the vines grew up. The foliage was thin and didn't shade it normally. This exposed the fruit to more direct sun and some of them developed sunscald. Sunscald is a white or yellow area on the fruit and can render it inedible. Though growing upside down is supposed to shade the fruit with the additional mass of the growing container, I didn't find that to be the case. The plants in the ground shaded the fruit well.
The bigger mass of the plants in the raised bed raised the overall temperatures near the plants and that may have helped produce more flowers. I also saw more bee and fly activity near these plants than in the hanging containers. That may also help explain why more fruit developed in the bed.