Although a very small difference, the image on the left, in LOG has a bit more blue cast on the skin and foliage, compared to the image on the right (LIN), where both scopes where pretty much in the same place.

Moreover, the difference between Log and Lin nodes comes when using Gain (Lin) vs. Offset (Log) for exposure adjustments.

On this example we can see that the top of the curve reaches somewhere around level 768, however, the shadow part of the curve is completely crushed when using the Offset wheel in Log space.

However, when using the Gain in Linear space, when reaching a similar level of 768, the shadows are completely preserved whilst the rest of the image is affected in a similar way, perhaps even in a more regular curve.

Finally, the difference to using Gain in Log space is as seen above, when reaching the same level of 768, the reduction in exposure is considerably lesser and the curve behaves differently.

This of course doesn’t indicate that between Gain in linear and Gain in Log one is better than the other, the effects one can achieve are clearly different, however, the Gain control wheel in linear is superior to the Offset in Log in the sense that it doesn’t crush the blacks. Once again, using the Offset wheel may be a better choice when one wants to affect the entire tonal range of the image, including the blacks and shadows, but for my practice when adjusting exposure, I will most likely start using Gain in Linear Gamma and possibly for white balancing too, in order to avoid crashing any particular portions of the image or channels.

Source: Cullen Kelly (https://www.youtube.com/watch?v=8OOOSo-ZgZo)