Carbon emission quota allocation plays a critical role in carbon emission reduction in an efficient and economic manner. However, the scientific assessment of carbon quota allocation schemes and thus making a reasonable decision depending on preference still confuses relevant decision makers. This study proposes a performance analysis framework for carbon quota allocation schemes by using a nonparametric frontier analysis approach from the perspectives of economic growth and energy conservation. Then, we apply this approach to evaluate the relative economic and energy conservation performances of 15 allocation schemes by reallocating the 2015 Chinese provincial carbon emission quotas, each of which is constructed via a combination of equity, grandfathering, efficiency and ability to pay principles. The results show that the proposed allocation scheme that integrates efficiency and the ability to pay principles is the best option, realizing approximately 6.78% outputs increase and 3.01% energy conservation relative to the actual 2015 emission scenario. We also show that the best scheme is linked to total quotas; the scheme considering only the equity principle is superior to others, while the total quotas are reduced by 10%. The study provides not only a theoretical tool, but also empirical evidence for the construction of China's carbon quota allocation scheme.