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We have observed several emission lines of two Nitrogen-bearing (C₂H₅CN and C₂H₃CN) and two Oxygen-bearing (CH₃OCH₃ and HCOOCH₃) molecules towards a sample of well-known hot molecular cores (HMCs) in order to check whether the chemical differentiation seen in the Orion-HMC and W3(H₂O) between O- and N-bearing molecules is a general property of HMCs. With the IRAM-30m telescope we have observed 12 HMCs in 21 bands, centered at frequencies from 86250 to 258280MHz. In six sources, we have detected a number of transitions sufficient to derive their main physical properties. The rotational temperatures obtained from C₂H₅CN, C₂H₃CN and CH₃OCH₃ range from ∼100 to ∼150K in these HMCs. The total column densities of these molecules are of the order of ∼10¹⁵-10¹⁷cm^–2. Single Gaussian fits performed to unblended lines show a marginal difference in the line peak velocities of the C₂H₅CN and CH₃OCH₃ lines, indicating a possible spatial separation between the region traced by the two molecules. On the other hand, neither the linewidths nor the rotational temperatures and column densities confirm such a result. The average molecular abundances of C₂H₅CN, C₂H₃CN and CH₃OCH₃ are in the range ∼10^–9-10^–10, comparable to those seen in the Orion hot core. In other HMCs Bisschop et al. 2007A&A...465..913B found comparable values for C₂H₅CN but values ∼2.5 times larger for CH₃OCH₃. By comparing the abundance ratio of the pair C₂H₅CN/C₂H₃CN with the predictions of theoretical models, we derive that the age of our cores ranges between 3.7 and 5.9x10⁴yr. The abundances of C₂H₅CN and C₂H₃CN are strongly correlated, as expected from theory which predicts that C₂H₃CN is formed through gas phase reactions involving C₂H₅CN . A correlation is also found between the abundances of C₂H₅CN and CH₃OCH₃, and C₂H₃CN and CH₃OCH₃. In all tracers the fractional abundances increase with the H₂ column density while they are not correlated with the gas temperature. On average, the chemical and physical differentiation between O- and N-bearing molecules seen in Orion and W3(H₂O) is not revealed by our observations. We believe that this is partly due to the poor angular resolution of our data, which allows us to derive only average values over the sources of the discussed parameters.