In which technique atomic absorption or atomic emission is flame temperature stability more critical?

Atomic emission  
There are two broad methods of using atomic spectroscopy to identify the elements present and their quantities. That being atomic absorption where light of a known wavelength is absorbed by atoms suspended within a flame and atomic emission where the atoms are excited by energy and emit light of known wavelengths that can then be measured.  
For atomic absorption to work, the main criteria is that the atoms be evenly dispersed throughout the flame and that they not be excited enough to spontaneously emit light themselves. As such a rather wide range of flame temperatures is acceptable and will cause only minor variations on the amount of absorbed light.  
For atomic emission to work, the flame needs to be hot enough to excite the atoms into spontaneously emit their characteristic wavelengths. Additionally, increasing the temperature will cause more light to be emitted even if the concentration of the atoms remains the same. So stable temperature control is vital for accurate measurements.