Conservative Republicans were generally isolationist on foreign policy and more open to New Deal measures that were good for urban areas, but not so much for rural areas.
Dixiecrats were unabashed hawks and tended to be hostile to New Deal measures that were good for urban areas, but very open to ones that modernized rural areas that had pretty much no electricity up to that point.
I would add some other areas where Southern Dixiecrats were very supportive of reforms and New Deal: transportation, agriculture (including irrigation), well - an education (for whites only, of course) too. That's why many of them were rated relatively high by liberal organisations in 1st phase of New Deal (1933-36). There were very few really economically conservative Democrats (George Terrell and his like) in Congress then. But on social and racial issues many Southern Democrats were to the right of even very conservative Republicans. And when FDR programs went further then simple "salvation from Depression" - southern opposition increased markedly.
And did southerners just adopt conservative economic views that Republicans held as they started switching affiliation? That's one part of the story I never really understood. The south would elect moderate-to-liberal senators up until the 1980s, such as Howell Heflin and John Sparkman.