raw vs jpg files

I was looking for a way to calibrate my monitor, or find a way to capture or color correct the pictures of my paintings that I took. There is xrite passport colorchecker which is a handy tool to check and adjust the color of your pictures. But the pictures have to be in raw files in order to do the adjustments efficiently and correctly. I remembered that I have raw file mode on my Canon G2 camera. So I decided to do a test. The 2 pictures are taken in the same light conditions (under flourescent light). The left is raw, middle one is jpg and the right one is the color corrected jpg. From comparing the color of the painting, even without adjustments I see the difference in accuracy color-wise. With the raw file I could do adjustments in Photoshop CS or Lightroom.

When I color corrected the jpg for the skin to be more reddish or orange, the lips which is red became even more red.