We present and compare in this paper new photometric redshift catalogs of the galaxies in three public fields: the NTT Deep Field, the HDF-N, and the HDF-S. In the case of the NTT Deep Field, we resent here a new photometric catalog, obtained by combining the existing BVrI and JKs with new deep U observations acquired with NIT-SUSI2, and which includes also the contiguous held centered on the z(em) = 4.7 quasar BR 1202-07. Photometric redshifts have been obtained for the whole sample (NTTDF + HDF-N + HDF-S), by adopting a chi (2) minimization technique on a spectral library drawn from the Bruzual and Chariot synthesis models, with the addition of dust and intergalactic absorption. The accuracy, determined from 125 galaxies with known spectroscopic redshifts, is sigma (2) similar to 0.08(0.3) in the redshift intervals z = 0-1.5(1.5-3.5). The global redshift distribution of I-selected galaxies shows a distinct peak at intermediate redshifts, z similar or equal to 0.6 at I-AB I 26 and z similar or equal to 0.8 at I-AB less than or equal to 27.5 followed by a tail extending to z similar or equal to 6. Systematic differences exist among the fields, most notably the HDF-S which contains a much smaller number of galaxies at z similar or equal to 0.9 and at z greater than or equal to 4.5 than the HDF-N. We also present for the first time the redshift distribution of the total IR-selected sample to faint limits (Ks less than or equal to 21 and J less than or equal to 22). It is found that the number density of galaxies at 1.25 < z < 1.5 is similar or equal to0.1 arcmin(-2) at J less than or equal to 21 and similar or equal to 1.0 arcmin-2 at J I 22 and drops to similar or equal to0.3 arcmin-2 (at J less than or equal to 22) at 1.5 < 2 < 2. The HDF data sets are used to compare the different results from color selection criteria and photometric redshifts in detecting galaxies in the redshift range 3.5 less than or equal to z less than or equal to 4.5. Photometric redshifts predict a number of high z candidates in both the HDF-N and HDF-S that is nearly 2 times larger than color selection criteria, and it is shown that this is primarily due to the inclusion of dusty models that were discarded in the original color selection criteria. In several cases, the selection of these objects is made possible by the additional constraints from the IR bands. This effect partially reflect the poor spectral sampling of the HDF filter set, and is not present in ground-based observations where a R-I less than or equal to0.5 color selection criteria may be applied. Finally, it is shown that galactic M stars may mimic z > 5 candidates in the HDF filter set and that the four brightest candidates at z > 5 in the HDF-S are indeed most likely M stars.
