In order to evaluate the quantum efficiency and to establish the mechanism of down-conversion processes in Bi3+ - Yb3+ and Ce3+ - Yb3+ co -doped YAG (Y3Al5O12) and GGG (Gd3Al5O12) garnets, direct measurements of quantum yield (QY) were performed along with studies of photoluminescence (PL), photoluminescence excitation (PLE), and photoluminescence decay kinetics. The studied materials have been prepared either in the form of powders synthesized by the sol-gel method or single crystalline films grown by the liquid phase epitaxy method. Concentrations of Bi3+, Ce3+ and Yb3+ ions in the studied epitaxial films were estimated using X-ray diffraction and optical absorption techniques. The obtained results testify a non -cooperative energy transfer mechanism for the Ce3+-Yb3+ co-doped YAG with a conversion ratio (which should be 2.0 for an ideal quantum cutting mechanism) less than 1.0. At the same time, for Bi3+-Yb3+ co-doped YAG and GGG this conversion ratio was found to be close to 2.0, suggesting quantum cutting via cooperative energy transfer from one Bi3+ ion to two Yb3+ ions.