I'm not interested in comparing if Adobe default color is more accurate between Fuji and Nikon, but but get a more accurate profile.
Sadly there's the rub. "Accurate" color and "film simulation" are mostly mutually exclusive. Fuji's film simulations are all about mimicking the color response of Fuji's old films, not about general color accuracy. Of course, some are more stylized than others, but I wouldn't consider any of them an attempt to stay "true" to the scene.
Personally I'd check out Adobe Neutral as a starting point, or at least Pro Neg Std. And if you're still seeing unnatural hue shifts, consider creating custom profiles for your common light sources.
The Camera Standard for Nikon works relatively well. The Adobe color for Fuji was not that good for this particular problem, that's why I didn't post it.
Overall I can get it closer if I manipulate the hue for Blue in the HSL panel; somewhere between minus 5-10 for Astia and minus 15-20 for Provia gets it close.
Profiles are a tough nut to crack. Generally speaking, the more "accurate" a profile is, the less pleasing/interesting it is initially. Hence the existence of Fuji's film simulations. You'll just have to pick whatever suits your needs for each photo, whether it be a Fuji sim or a neutral profile. Sorry, there's no silver bullet here.
You might be interested in Lumariver's "Profile-making Theory" portion of their manual:
http://www.lumariver.com/lrpd-manual/#profile_theoryEspecially the "Subjective color" sub-section:
http://www.lumariver.com/lrpd-manual/#subjective_color