Some wordplay may help: Dehydrate carbohydrates, freeze-dry fresh fruits.
There shouldn't be a problem in freeze-dried food. The freeze-dry process, while expensive and impractical for home users (small effective freezer units start at about 10k USD, used!) retains about 90% of the origonal nutritional value as well as texture after rehydrating. Freeze-dried food is actually quite tasty and is the preferred method for taste and consistency, and keeps vitamins from breaking down.
Dehydrated foods for the most part don't reconstitute well unless they're starch-heavy (noodles, beans, rice, potatoes, some powdered goods). Dehydrated meats (jerky) last a long time and retain flavor, but this method of food storage does not bode well for vitamins, especially in fruits and vegetables, since the water solution they subside in is evaporated (more vitamin loss than cooking).
As far as canning goes, its the middle-ground. You have to boil/cook the food to destroy bacteria, but keep a better consistency and flavor. Its also easier and cheaper to get started in, since freeze-dried food is expensive, and if bought in bulk (to reduce cost) you generally have to portion it out with a vacuum sealer (don't buy a cheap one) and/or use oxygen absorbers, unless you plan on serving an entire #10 bulk can of chili mac at once! XD
Edit: per health effects, there's nothing about freeze-drying that does anything to the food. Its just put in a VERY cold environment as all the air is sucked out with an industrial vacumn. Most dehydrated food is, well, dried, and most of the time salt is added to improve the process, so drink plenty of water!
edit on 10-4-2012 by TheQuantumAnomaly because: Addressed health concerns