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So the old demo has more NSFW content by virtue of covering more chapters overall.  There's no actual difference to the contents themselves though beyond the ability to more precisely control what you can view in a given playthrough.
So to be more specific, the demo features one setting that either enables all nsfw content or removes all of it.  The Playable Teaser allows you to choose between presets or fully decide exactly what you want to see. So specific things can be shut off so you won't encounter them if you don't want to while still including the NSFW material you would like to see.  Aside from that the actual scenes are the same and accessed in the same way across the two builds. 
I would say NSFW qualifies the same as story.  If that's the main thing you're looking to check out I would suggest playing the demo over the playable teaser.  However if there's specific fetish content you want to avoid, the PT can allow you to do that in trade off for not having chapter 1, 2, and 5.  Hope that helps!

Thanks for the reply. And yeah, that helps. I just wasn't sure if the new PT version would have new/more NSFW content not only because it's a newer version but also because you mentioned it had more enemies.

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Yeah the enemies in Project Red aren't a big contributor to the NSFW content unlike most games.  Overall the PT is more focused on combat and movement updates.