Tegal ... I do not know what editor you have but I took your first image and opened it with an adjustment layer/curves above it and immediately I saw a problem that it didn't occupy the whole of the range of tones. I brought the black and white to where the layer was showing and the result was similar to your revised version. I believe from what Manfred has written recently this is something like organizing the black and white points in Adobe but since I do not use Adobe I cannot be more specific.
I follow this process of checking my black and white levels in most shots I take and usually following the programme's suggestion improves the shot. I often do this when thinking about shots I see here on CiC.
further tried something to hopefully explain myself better since I doubt you have my editor
placing the color picker tool over the dark wing of the left-hand bird I get a reading of 38 and off the sky 178 .... the adjustment layer corrections change this to 0-255 ... we are reading on a scale of 0-256 from black to white The correction makes the birds' darker and the sky whiter
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