Results are presented on a complex study of field electron emission (FEE) and structural correlations for nanocrystalline diamond and nitride films. It was found that all the samples studied showed similar dependences of the Fowler-Nordheim work function and effective emitting area on the threshold emission field. Besides it was generally observed that FEE occurred at nanosized regions on the boundary of high and low conducting areas, and peaks of the emission intensity were associated with a lowered surface electron potential. Based on the experimental data, the following mechanism of low-FEE from the materials studied can be supposed. Electrons are transferred from the conducting channel into a vacuum through the low-dimensional region where the emission probability is high due to the quantum well effect. A physical model of the electron escape from a quantum well was analyzed. As follows from the estimations, the quantum size effect, being combined with a moderate field enhancement (the field enhancement factor beta=10-100), allows us to explain the observed variation in the energetic parameters for the samples studied. The function of the insulating grains is mainly to support the conducting channels in the sample body. Also, the grains can fulfill an additional function of the heat sink.