Its not that simple and its not always possible if color info is not there, it wouldnt look the same and as natural, i tried to bring back contrast and contrast is spread differently on first and second pic, even with curves they wouldnt look the same.What I see in your screengrabs, bwwd, is totally adjustable in post. I could make those images match completely with a few minutes in Color or After Effects.
In theory its simple but in practice its not.When you record with contrast on 0 then you see a lot more colour on human face, sometimes cheeks are reddish but with contrast on -4 you wont get it, even grass is plain green without contrast.If you add saturation then colours are still the same, theres no variation of colour on face, theres just more of the same plain dull colour.
For me first pic looks very ugly and camcorderlike.