As always, it depends on your taste, and I consider both approaches perfectly fine, and equally worthwhile, when done well.
Personally, I always write in an alternate world, even when there are no speculative elements involved (although, usually, there are). I do so for three main reasons:
- I can build the world in the perfect way to portray the story. Why confine myself to the limitations of ours?
- I do not run into issues of accuracy, just like you mentioned. I created that world, and I know everything about it perfectly. Ain't nobody correctin' me then.
- I just love world-building, and the epic nature of it. I feel it adds another layer to the tale being told.
Of course, this approach requires more world-building, both behind the curtains, and in the story-telling. But as I said, I love it.
However, I can see how people who know some event/war/era very well, would feel the urge to write about it. I do not find it less magical, if done well. I just find it harder to do well, and personally, less exciting (to write--not to read).
I just hate being limited.
Anyhow, that really depends on you, your taste and your capabilities. I wish you luck, whatever you choose!