The logic that no Red Russia means no Nazis is something I find flawed. Good ol' anti-Slavic racism and antiSemitism was far more crucial to getting working class votes than fear mongering about the Reds, which worked with the elites.
Of course, White Russia does not mean ALL OF RUSSIA is white. There could have been an agreement reached in the Civil War where the Whites get the South and most of Siberia while the Reds get the rest. If this happens, the tide could change.
But to your main question, saying that White Russia exists with Soviet borders and the invasion goes ahead as planned, I give the Germans the edge because Russia would be less able to industrially support itself, even if there is more qualitative officer composition. Still, Western aid might be even forthcoming than OTL, and Russian manpower might be better than it was with the Stalinist massacres and famines, not to mention of course a better officiered army and the Church as a symbol to rally around, which was indeed effective in the past. It would be a total war of annihilation just as OTL, so Russian motivation and willingness to accept horrible losses would be just as high. I just don't know if they'd be able to win with the lack of industrialization of OTL, which was forced and not something I think White Russia would do.