The vast amount of data being collected about individuals has brought new challenges in protecting their privacy when this data is disseminated. As a result, Privacy-Preserving Data Publishing has become an active research area, in which multiple anonymization algorithms have been proposed. However, given the large number of algorithms available and limited information regarding their performance, it is difficult to identify and select the most appropriate algorithm given a particular publishing scenario, especially for practitioners. In this paper, we perform a systematic comparison of three well-known k-anonymization algorithms to measure their efficiency (in terms of resources usage) and their effectiveness (in terms of data utility). We extend the scope of their original evaluation by employing a more comprehensive set of scenarios: different parameters, metrics and datasets. Using publicly available implementations of those algorithms, we conduct a series of experiments and a comprehensive analysis to identify the factors that influence their performance, in order to guide practitioners in the selection of an algorithm. We demonstrate through experimental evaluation, the conditions in which one algorithm outperforms the others for a particular metric, depending on the input dataset and privacy requirements. Our findings motivate the necessity of creating methodologies that provide recommendations about the best algorithm given a particular publishing scenario.