The ex-post assessment of institutional performance has been applied to allocate scientific and technological (S&T) resource to universities and public research institutes. However, over-emphasis on particular types of performance could lead to unintended results and harm the science system. This research assesses the performance of these universities and public research institutes using 'technical efficiency' and their potential using 'capacity utilization', which are obtained by data envelopment analysis methods. Moreover, a comprehensive S&T resource allocation framework is proposed, where the organizations can be classified into four groups according to their performance and potential assessment results. An empirical study is conducted using the data of 58 Chinese research institutes from 2011 to 2018. Results indicate different patterns in the distribution and evolution of the performance and potential of these research institutes. The approaches proposed by this research are expected to complement existing performance-based S&T resource allocations.