When burning waste the steam does not become so hot. When the cold end is in constant temperature, the efficiency is higher, if the steam is hotter. (Carnot ia to blame) When burning natural gas the steam can be much hotter than when burning municipal waste.
In chp the steam goes first to the turbine (for electricity), then for district heating. When going to district heating, the water is somewhere near 100 degrees celsius hot, sometimes 115 (pressurised, 1 bar) in cold winter time. So the temperature difference of the turbine input and output is determined by the input heat. I guess, that the steam with natural gas is about 550 degrees and pressure about 200 bars and with waste about 500 and 150 bars. So the total efficiency with waste is lower.