Periodically I receive correspondence or read media articles about (or witness myself) controversies involving the feeding of cats. Frequently, the situation was brought to the attention of anti-cat folk due to the perceived mess of the use of paper plates, or the alarm caused by seeing a caretaker surrounded by five or six cats in a place where people are surprised to see cats exist (a workplace loading dock, a restaurant dumpster area, etc.).
Primarily due to lack of time, and the fact that I've often been caring for cats in areas where I don't want to be seen, I have always fed my cats dry food.
The advantages of dry food are these:
You can build a covered feeding box that looks like a tool box or storage box, that will keep out prying eyes as well as birds. If elevated, it will keep out skunks and deter (but not eliminate) oppossums.
Dry food can be fed in a heavy plastic bowl and need not be washed daily. Wet food containers must be discarded (if paper) or washed daily (if plastic/glass).
Dry food is not as attractive to flies as wet food.
Dry food can be put out in the morning, and cats will visit slowly throughout the day, rather than drawing them in a mass to compete for that wonderful tasty wet stuff. I know with my own personal cats, the bowl of nutritious dry sits there with one cat at a time visiting it, whereas when I pull out the wet food (as a treat for all when Nick comes in for the evening) I have a slightly alarming swarm of cats in my kitchen. Use of dry food reduces the "alarm factor" among witnesses.
There are disadvantages to dry food as well. These include the fact that BECAUSE food is available all day, there is always evidence of cats being fed. (If you feed wet food, you are there and gone, and if you pick up the plates, once you are gone there is no evidence you were there). Also, food remaining after dark can become an attractant to wildlife. However, in my experience, a human doling out tasty stuff to a herd of cats once or twice a day is more likely to be noticed that a human filling a bowl in a feeding station in the morning and immediately leaving.
Also, if you are specifically trying to tame up cats so you can home them, wet food is a better option.
I know people really like to give feral cats the extra luxury of wet food, but in some situations it can actually increase stress (competition with other cats for wet food at a limited time window rather than just waiting one's turn for dry that will be there all day) and it does increase public notice and the alarm factor.
I know myself when I am trying to find the person responsible for a colony in a neighbor, I just look for paper plates. Nothing says "feral colony" like a sea of paper plates in someone's back yard.
Yes, it is true that if you feed dry, you won't see "your" cats as often. They are less likely to come out to greet you if they know food is available all day (Be sure to feed only so much that most is gone by "wildlife hour" at dusk). If the cats are in a secure area, by all means feed wet as dinner or a treat if you like.
But in areas where cats are at risk or the public or neighbors may complain, consider just feeding good quality dry food, and save the wet food to medicate or trap cats.
Please feel free to post advantages/disadvantages of different foods in the comments. As a "dry feeder" I may not be aware of additional advantages of feeding wet food.