There isn't a 'kit' that can test accurately for Nitrogen. As a matter of fact, most state extension tests don't include nitrogen, either. It is simply too volatile, unstable.

You don't mention what part of the country you are from, but it would be worthwhile seeing if your state's extension department offers reasonable, reliable soil testing.

The availability of Nitrogen in soil can be highly dependant on soil temperature, which determines bacterial activity. So when you take the test can influence the results. Excess levels of Potash (K) can create apparent N deficiencies.

Many labs do test for nitrogen compounds, and there are multiple classes of tests: ammonia nitrogen, nitrates, several different nitrites...

The N test in this kit apparently isn't testing for ammonia nitrogen, because it does not indicate high N for household ammonia.

Without participation in a 3rd party conformity assessment program, there is no assurance that laboratory test results are reliable. If you doubt the reliability of home test kits, you should also doubt the reliability of laboratory test kits.

Anyway, has anyone here compared home test kit results with laboratory results for the same soil?

Yes. It's hilarious.

Which kits?

I have no idea. Homeowners will call and say, "I got 'such and such' results from a kit I bought at" (fill in the name of a big box store or local nursery) "but I'm not sure it's right."
Either that or they jot down the results they got and bring them in with the sample. The values they report are typically a million miles from what we determine.

Let's not forget soil nitrite determinations now. Let's see, how does a lab assure that their results are precise,accurate and reproducible? With a good QC program, duh! You know, like using U.S. Bureau of Standards standards, blanks, and duplicates in analytical runs etc., etc., etc.. Third party?