The field emission properties of chemical vapor deposition (CVD) diamond thin films are investigated by measuring the field emission I-V characteristics, the emission site density and the field emitted electron energy distribution. The results are discussed with regard to field emission due to negative electron affinity (NEA) and classical Fowler-Nordheim emission due to geometrical field enhancement. The requirements on the diamond films for NEA mediated field emission are discussed. These requirements are high resistivity, low defect density and few grain boundaries. We show that diamond films matching these requirements are actually bad field emitters. On the other hand we show that the films exhibiting good field emission properties are just opposed to the above mentioned requirements, they exhibit low resistivity, high defect density and many grain boundaries as they are of nanocrystalline nature. The good emitting CVD diamond films are grown on p-type Si(100) using plasma enhanced CVD at substrate temperatures around 950 degreesC and a gas mixture of 5% CH4 in H-2. Using the example of multiwalled carbon nanotube emitter (MWNT) we show how the emitter work function and the local field at the emission site can be determined independently by measuring the field emitted electron energy distribution. For MWNT we find a work function of 4.9 eV and a local field of 2500 V mum(-1) (for an emission current of the order of 10 pA). In the case of nanocrystalline CVD diamond emitter we find work function values around 6 eV and local electric fields again of the order of 2500 V mum(-1). The electronic structure of the nanocrystalline CVD diamond field emitters is investigated using standard photoemission spectroscopy and simultaneous photoemission and field emission spectroscopy. From the presented measurements we can clearly relate the low field electron emission of the investigated nanocrystalline diamond films to classical Fowler-Nordheim tunneling due to local geometrical field enhancement.