Using ideas and tools of complexity science we design a holistic measure of \textit{Scientific Fitness}, encompassing the scientific knowledge, capabilities and competitiveness of a research system. We characterize the temporal dynamics of Scientific Fitness and R\&D expenditures at the geographical scale of nations, highlighting patterns of similar research systems, and showing how developing nations (China in particular) are quickly catching up the developed ones. Down-scaling the aggregation level of the analysis, we find that even developed nations show a considerable level of inequality in the Scientific Fitness of their internal regions. Further, we assess comparatively how the competitiveness of each geographic region is distributed over the spectrum of research sectors. Overall, the Scientific Fitness represents the first high quality estimation of the scientific strength of nations and regions, opening new policy-making applications for better allocating resources, filling inequality gaps and ultimately promoting innovation.