Socio-economic development and the concept of the tourist function of areas are multidimensional socio-economic phenomena, the diagnosis of which is particularly important in various comparative studies regarding EU countries. Measurement based on GDP per capita, widely used in the assessment of the socio-economic level of development of countries, does not include many aspects of this development in its construction. Similarly, the level of development of the tourist function cannot be assessed by means of one universal measure. Both categories should be treated as complex phenomena, which are influenced by many different factors. The aim of this article is to compare and statistically assess two complex phenomena, i.e. level of socio-economic development and level of tourist function development in 28 European Union countries. Linear ordering of EU countries was carried out using the TOPSIS method on the basis of diagnostic variables determining individual complex phenomena in 2016. Values of the overall synthetic measure were also indicated, taking into account all diagnostic variables. Rankings of EU countries were built and four typological groups of countries with high, medium-high, medium-low and low level of development were created. Discriminant analysis indicated variables that have the greatest impact on the classification of EU countries in terms of the level of socio-economic development and level of tourism function development. A linear econometric model with synthetic variables was also constructed, and it was determined which of the synthetic measures is relatively more important in describing the shaping of the overall synthetic measure. The quality of the work is increased by the use of many different statistical and econometric methods, as well as methods from the field of Multidimensional Comparative Analysis. Thanks to this, it is possible not only to deepen the assessment of the studied phenomena, but also to obtain more objective results. Conclusions from the research may be a basis for proper management in the field of socio-economic development as well as for the development of the tourist function of EU countries. They can also be used for appropriate allocation of financial support for countries within the framework of the EU cohesion policy and in determining the tourist specialization of countries.