A lot of detail is being lost in the top image and it is overall warmer than the bottom image.  I would agree that the second image is more natural-looking to the eye.  Quite some time ago when I was researching Gamma correction to understand it better, I came across posts that MACs have a different Gc than PC video output.  IIRC, Gc for a MAC was 1.5 as opposed to 2.2.  This was quite some time ago and I don't know if this has been standardized since then and if it has any bearing on monitor calibration.  FWIW, that top image is exhibiting clipping on the bright end of its output.  As I mentioned, you're losing detail in your shadows and blowing out the highlights.  Technically correct does not necessarily mean visually pleasing to the human eye.  That's why there is post-production.