1: In Eview 6, three models are used for random effects model:Swamy-Arora (default), Wallace-Hussain and Wansbeek-Kapteyn. Each method results in a different variance and a different p-value of the Hausman test, which means perhaps at least one of the results from those three methods could be closest to the Stata
2: the differences are possibly due to the way that degrees of freedom are factored into the variance/sd calculations. Stata often uses a different DoF correction from EViews.
Hope it works