There are plenty of studies comparing combustion method to the Kjeldahl method going right back to the 80s (Search the AOAC journal), and the combustion method compares very well.
Having used both methods in my murky past I can say that I would never want to use the kjeldahl method again!
I was using a LECO machine latterly and it was faster and more accurate, as well as a lot safer to work with. It was heavy on consumables - gas, filters, etc but still the better way to go I thought.
Note: It's been a while since I did much food chemistry so maybe the more automated kjeldahl machines are better to work with now!