An article at slate.com describes how food labs measure calories, and where the calorie numbers come from on food labels. It's good for background info on the process.
Unless you have a remarkably well-stocked and well-equipped lab in your basement, you're not going to be able to test vitamin content at home. As far as I can tell, literature dealing with these topics is aimed at industrial users and/or academic papers. See, for example, this abstract on testing vitamin D using liquid chromatography [pdf].
Furthermore, you can't even really trust the labels on the foods you buy to be accurate: producers can just use the values from government tables. So if there are differences, they won't necessarily be reflected on the label of a particular batch of food that you've purchased.
I know of no literature regarding "home grown" vs "supermarket", but there is info on the nutritional content of organic vs conventionally grown fruits and veg:
- This article at the Mayo Clinic says "a study" (uncited) found that organic and conventional are comparable for nutrition.
- The same Mayo Clinic article says that the USDA (uncited) has found that organic foods contain significantly fewer pesticide residues than conventional.
This report [pdf] for the UK Food Standards Agency might be the one referenced by the Mayo Clinic article above. They surveyed the literature and found:
There is no good evidence that increased dietary intake, of the nutrients identified in this review to be present in larger amounts in organically than in conventionally produced crops and livestock products, would be of benefit to individuals consuming a normal varied diet, and it is therefore unlikely that these differences in nutrient content are relevant to consumer health.
There were small differences in the content of some things in some foods.
Another survey study out of New Zealand [abstract] finds that the "findings are inconsistent".
Yet another survey study [abstract] found that there are significant differences in the levels of some nutrients.
Local (backyard!) food may be more nutritious for a few reasons: cultivars are selected for taste and nutrition above yield and transportability, processing is reduced or eliminated, and damage from transport is reduced or eliminated.
Unfortunately I don't see any literature that can give you concrete guidance or hard numbers.
For what it's worth, my personal experience is that home-grown and locally-produced food has far superior flavor and texture compared to supermarket food from "far away". (And we don't have to worry when there are massive recalls on lettuce, tomatoes, beef, eggs, etc.)