What a GIF is, and what it costs
GIF is limited to 256 colours per frame. A photograph saved as GIF has been through a palette reduction that is visible as banding in gradients, and converting to JPEG cannot restore the colours that were dropped.
It also has only fully-on or fully-off transparency: a pixel is either opaque or invisible, with nothing in between. That is why GIF logos have jagged edges against a background other than the one they were made for, and why PNG replaced it for static images.