Well they are/were both dictatorships.
That's pretty much it.
The Third Reich had freedom of speech, religion (although German officers were all Christian), the right to bear arms, no slavery (unless you count the Jewish work camps), modern technology. I would agree that the way life is lived...
This is what I think of the DLCs:
HH: Interesting for lore and new weapons and enemies. Pretty fun and short DLC.
OWB: Definitely the best in terms of gameplay. It's just fun. Trying to convince your brain to come back into your body is the kind of thing that makes Fallout the best series ever...
I'd like to think I would be like the Courier and I'd join the Legion. Most likely I would be a scavver (prospector if you wanna sound fancy) or just live in a settlement.