Like so many fads often do, the vertical gardening fad has become trendier than it really should be. It certainly has practical applications, and is very appealing in the right situations. However, in the wrong situations, it can be more problematic than it is worth.
Vertical gardens can shade and insulate exposed walls, but really do little more than strategically placed shade trees, large shrubbery or even trellised vines can do in that regard. The disadvantage of vertical gardening is that it can hold moisture against the affected walls, and can promote rot if the planters are not installed properly. Planters over windows or decks drip just like any other planters do, staining or dirtying whatever is below. Only free standing vertical gardens (that are not attached to a wall) or those on concrete walls that are not susceptible to rot will not cause such problems.
Water borne pathogens (diseases that disperse in water) can proliferate more in vertical gardens because they get carried with the natural flow of water from top to bottom. Wherever any such disease gets established on a vertical garden, it will likely get carried to everything below. In the ground, such diseases spread slower since they only travel as far as water flows or gets splashed.
The obvious advantage to vertical gardening is that it makes it possible to grow many more plants in very limited space, which is excellent if there is no open ground for vegetable gardening. It can also be a great way to display plants like orchids and certain bromeliads that are more appealing if they hang from above. Staghorn ferns cling to walls naturally.
Another advantage is that vertical gardening can be so aesthetically appealing and unique. Vertical gardens of small, densely foliated succulents hung like tapestries to adorn exterior walls are so much more interesting than simple vines or shrubbery used to obscure such walls. Northern exposures that are too dark for most plants can be adorned with ferns.