It gives more flavor, and disassociates that regime from todays Germany.
I can see that and you are walking a fine line. Many describe the war today as the war against 'Nazi Germany' not the war against 'Germany'. I think 'Third Reich' sounds better, but not sure if the causal gamer today would 'Get it' as being Germany. The ignorance level in the U.S. is very high, but I am not sure if that is so true for people who play Paradox games.