The analogy is not a good one on two counts.I thought it was pretty well established that TL-191's USA is the USSR to the CSA's Nazi Germany,
1) The USA had territorial claims on the CSA that the USSR did not on Nazi Germany.
2) The differences in technology between the USA and CSA were less than that between the USSR and Nazi Germany.
I would thus take such an analogy with a pinch of salt, especially if it was made by Turtledove
Not necessarily if they carve the world into spheres of influence; after all ideologically they are not very different.I'd always imagine a cold war arising between the European CPs and the USA after Japan is dealt with.
As a start the spheres would be Latin America to the USA and North Africa and South West Asia to Germany. Sub Saharan Africa could be split with the west coast going to the USA and east to Germany now it or its Ottoman proxy own the Suez Canal. East Asia is easier to reach from the USA to it gets it whilst the Germans take South Asia includes the Dutch East Indies. Australasia falls to whoever can be bothered about it.
Both sides can draw who resources they need from their sphere without bothering the other and thus have no need for the major arms race on our TL. Instead they can drive for the Moon (the Germans certainly would) and beyond.
On course minor powers in each sphere would have to be slapped down, but they would not on their own.