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We summarize the latest R&D state-of-art of Ce3+ and Pr3+-doped mixed (LuxY1-x)3Al5O12 (LuYAG) garnet scintillator crystals and compare their properties with those of Lu3Al5O12 (LuAG) and Y3Al5O12 (YAG) single crystal analogues. Light yield, energy resolution and proportionality were studied under radioisotope excitation within 8-1300 keV energy range. The highest light yield of about 27000 ph/MeV is obtained in the newest prepared Ce3+ -doped LuAG crystals while up to 17000 ph/MeV was measured in the Pr3+-doped ones. On the contrary, the energy resolution and proportionality are noticeably better in the Pr3+ -doped crystals. Mixed Ce3+- or Pr3+-doped LuxY1-xAG (x=0.9-1) crystals show comparable light yield and energy resolution compared to those doped pure LuAG, but the content of slow components in scintillation pulses lower.