It seems that Chinese competition for SLS will be launched not before end of next decade.
China News Service press agency announced that new Chinese super heavy rocket will not be launched since 2030. According to Source close to China Academy of Space Technology (CAST) for the moment priority for CAST will be developing Long March 5 rocket which will open new possibilities for establishing China space station. Source also mentioned that crucial for developing new generation of super heavy rockets is achieving general technology and engines for Long March 5 first. Long March 9 is still considered by Source as a project in very early phase. According to China News, it was confirmed that Long March 9 will exceed in dimensions Long March 5, but for the moment China is not in possession of necessary technology for such ambitious project. Rumor about first launch of Long March 9 on 2028 has not been confirmed - CAST is not even considering launch before 2030. In general assumptions, Long March 9 will have around 9 m od diameter, weight at 3000 t and payload capacity at least 130 t. It seems to be competition for SLS which is similar in diameter (8.4) and comparable potential payload capacity for LEO missions at 130 t. Long March 5 with its maximal payload capacity of 10 t could be comparable for Delta IV Heavy and Atlas V not for SLS, and it seems that China will remain without any potential launch vehicle for manned mission to the Moon until 2030.