What do you get if you use the ORTHOREG procedure instead of PROC REG to fit the fixed effect model in SAS? If you get coefficients which differ from those produced by the REG procedure, then your data are probably ill conditioned, making it very difficult to get exact results.
The ORTHOREG procedure is designed to produce estimates for a fixed efffect model with more accuracy than the estimates produced by the REG procedure. There is no equivalent SAS procedure which produces highly accurate results for a mixed model. I can't tell you what option to use in STATA to produce highly accurate results.