Air pollution is a great concern because of its impact on human health and on the environment. Statistical models play an important role in improving knowledge of this complex spatio-temporal phenomenon and in supporting public agencies and policy makers. We focus on the class of hierarchical models that provides a flexible framework for incorporating spatio-temporal interactions at different hierarchical levels. The challenge is to choose a model that is satisfactory in terms of goodness of fit, interpretability, parsimoniousness, prediction capability and computational costs. In order to support this choice, we propose a comparison approach based on a set of criteria summarized in a table that can be easily communicated to non-statisticians. Our proposal - simple in principle but articulated in practice - holds true for many environmental phenomena where a hierarchical structure is suitable, a large-scale trend is included and a spatio-temporal covariance function has to be chosen. We illustrate the details of our proposal through a case study concerning particulate matter concentrations in Piemonte region (Italy) during the cold season October 2005-March 2006. From the evaluation of the proposed criteria for our case study we draw some conclusions. First, a model with a complex hierarchical structure is globally preferable to one with a complex spatio-temporal covariance function. Moreover, in the absence of suitable computational resources, a model simple in structure and with a simple covariance function can be chosen, since it shows good prediction performance at reasonable computational costs.