Albeit some studies discussing the performance of the hybrid chiller based CCHP systems and the only an absorption chiller (AC) based CCHP systems from different perspectives, however, there is still lack of theoretical studies focus on the comparison of these two types CCHP systems and screen out the suitable users for CCHP systems. In this research, instead of the case study, the dimensionless energy-matching parameters and map are extracted and designed to quantitative analyses the matching performance for these two systems. Energy saving rate (ESR), CO2 emission reduction (CO2ER), and operation cost reduction (CostR) for these two systems under different operation strategies are compared based on two situations: 1) the redundant electricity that systems produced neither can sold back to the grid, nor can used by the electric chiller; 2) the redundant electricity can used by the electric chiller. According to the comparison, the comprehensive operation strategy maps are drawn to guide systems running in the off-design condition, which are suitable for different energy-matching performance in ESR, CO2ER, and CostR. Meanwhile, an optimisation operation strategy (FOL) is proposed for the hybrid chiller based CCHP systems and its suitable application scenario is also calculated based on the operation strategy map. Finally, boundaries of suitable user demands for CCHP systems (ESR > 15%) in China are applied during summers and winters.