We report a broad comparative analysis of the spectroscopic and laser properties of solid solution Lutetium-Yttrium Aluminum Garnet (LuYAG, (LuxY1-x)3Al5O12) ceramics doped with Yb. The investigation was mainly aimed to assess the impact of the Lu/Y ratio on the Yb optical and laser properties. Therefore we analyzed a set of samples with different Y/Lu balance, namely 25/75, 50/50 and 75/25, with 15% Yb doping. We found that the Yb absorption and emission spectra changed from YAG to LuAG when gradually increasing in Lu content. Regarding the laser emission, remarkable results were achieved with all samples. Maximum output power was 8.2 W, 7.3 W and 8.7 W for Y/Lu balance 25/75, 50/50 and 75/25 respectively, at 1030 nm; the slope efficiency and the optical-to-optical efficiencies approached or exceeded 60% and 50% respectively. The tuning range was investigated using an intracavity ZnSe prism. The broadest tuning range (998 nm to 1063 nm) was obtained with Y/Lu balance 75/25, whereas the emission of the other two samples extended from 1000 nm to 1058 nm. To the best of our knowledge, this is the first comparative analysis of Yb:LuYAG ceramics or crystals as laser host across such a broad range of Y/Lu ratios.