Comparison is a powerful tool for decision support. Many measures have been proposed for comparing two metric spaces, but they do not consider the data dispersion in each metric space. Furthermore, no dedicated measure has yet been proposed for comparing two metric spaces containing elements belonging to various subtypes of a global datatype. In order to attenuate the aforementioned limitations, this paper proposes a new technique for comparing two metric spaces. More formally, given a metric space X, histograms are used for performing a gradual analysis of the data dispersion inside the neighborhood of each element of X. This is a refinement of the neighborhoods' analysis realized in an existing work. Then, another existing technique is used for associating one hidden Markov model X with X such that X learns the bin values and the visual shapes of the histograms derived from the instances in X. Meta-data derived from X are then saved as the components of a descriptor vector X associated with X. Finally, the comparison between two metric spaces is performed through the comparison of their respective associated descriptor vectors using existing distance or similarity measures between two vectors. The proposed approach inherits the accuracy and the efficiency of the existing techniques on which it relies. Therefore, the experiments realized in this paper are only intended to show how it can be used for comparing particular metric spaces containing geolocations or stars in the celestial sphere.