Digitalization and technological advancement, referred to as the Fourth Industrial Revolution (Industry 4.0), results not only in technological innovation but also in the changes in society and public awareness. One such tendency is the demographic aging, which implicates two concerns: the instability of the public pension systems and the social awareness related with the risk of major reduction of benefits in contrast to the expectations and the need for the additional private pension security. The research has aimed to identify the opinions and attitudes of the students from Poland and Ukraine in respect to the broadly understood issues of the old age security, as well as to recognize the prospective differences in this field between the researched populations. The relevant research was conducted using the PAPI method in the years 2018–2019. Within the framework of the research, nine specific hypotheses were presented concerning the attitudes towards the selected aspects of the pension schemes and old-age security. The results were compiled in the form of the semantic differential, and the Mann-Whitney U test was utilized to verify the significance of the differences in the distribution of the answers given by the students. Those served as the basis for formulating the conclusions regarding similarities and differences in the opinions expressed by young people studied populations.