Recent studies have indicated that the HCN-to-CO(J=1-0) and HCO+-to-HCN(J=1-0) ratios are significantly different between galaxies with AGN (active galactic nucleus) and SB (starburst) signatures. In order to study the molecular gas properties in active galaxies and search for differences between AGN and SB environments, we observed the HCN(J=1-0), (J=2-1), (J=3-2), HCO+(J=1-0) and HCO+(J=3-2), emission with the IRAM 30m in the centre of 12 nearby active galaxies which either exhibit nuclear SB and/or AGN signatures. Consistent with previous results, we find a significant difference of the HCN(J=2-1)-to-HCN(J=1-0), HCN(J=3-2)-to-HCN(J=1-0), HCO+(J=3-2)-to-HCO+(J=3-2), and HCO+-to-HCN intensity ratios between the sources dominated by an AGN and those with an additional or pure central SB: the HCN, HCO+ and HCO+-to-HCN intensity ratios tend to be higher in the galaxies of our sample with a central SB as opposed to the pure AGN cases which show rather low intensity ratios. Based on an LVG analysis of these data, i.e., assuming purely collisional excitation, the (average) molecular gas densities in the SB dominated sources of our sample seem to be systematically higher than in the AGN sources. The LVG analysis seems to further support systematically higher HCN and/or lower HCO+ abundances as well as similar or higher gas temperatures in AGN compared to the SB sources of our sample. Also, we find that the HCN-to-CO ratios decrease with increasing rotational number J for the AGN while they stay mostly constant for the SB sources.