What are some of the scientific differences between them that I should consider? Will one be better than the other considering we do have the tan windows?
Hue Family - they're about the same, they're in the same hue family neighborhood. Nothing remarkably different.
Value - again, about the same.
Chroma - Simply White has more chromaticity or colorfulness.
Not that much more but enough so that it's not as neutral as Pure White.
Which explains the moments of creaminess you've noticed.
Since we're talking the yellow hue family, the chroma is yellowness.
The extra bump of chroma explains why Simply White has a higher LRV - it is literally more reflective than Pure White which has a lower chroma. Again, not by much.
But the differences are enough to validate what you've observed. That Simply White is creamier and Pure White looks more gray (actually more neutral).
I would choose Simply White. Because I think it works better in the overall grand scheme and Pure White is a perfectly fine color of white but it's not one of my favorites.
Q