Detailed study of Stimulated Raman scattering (SRS) of 1.06- micrometers , 50-ps pulses in BaWO4 and KGW crystals was performed. Single-pass, double-pass and Raman cavity arrangements were compared regarding threshold intensity, conversion efficiency and pulse structure. Single-pass conversion efficiencies reached 25 percent for both BaWO4 and KGW. Double passing of the pump beam slightly improved the efficiency to 35 percent. Placing the BaWO4 crystal into a cavity and optimizing the performance by varying the output coupler spectral characteristics and the resonator length, 55 percent pump-to-first-Stokes efficiency has been obtained. The maximum of the Raman laser output energy was 3 mJ. The output consisted of 2-4 picosecond pulses at the 1180 nm wavelength. Dependence of the BaWO4 Raman laser output beam structure on the pumping energy was studied. The concentric ring profile, typical for transient SRS, was homogenized using a cyclic olefin polymer coated silver hollow glass waveguide. A similar study was performed with KGW crystal, for which the first Stokes wavelengths are 1159 nm or 1177 nm, depending on the sample orientation. Due to lower gain value, Raman laser energy reached 2 mJ and maximum efficiency was 30 percent. Based on our comparative study, a new BaWO4 crystal is highly suitable for utilization in the near IR picosecond Raman lasers.