Here's the first comparative photo - saved simultaneously as raw and jpeg, so the same photo at heart.
First, here is the jpeg file, cropped right into 797 x 443 pixels and following is the raw, imported into lightroom with exposure +.05, contrast +7, Clarity +5, Luminance Noise Reduction 48 and Color Noise Reduction 30. (without noise reduction, the image is fairly noisy - the picture was shot at iso 1600.
The colour handling of the printed fabric colours is pretty much the same, although there is a bit of gritiness around the colour edges that looks like it could be over sharpening or jpeg compression artifacts, look at the originals to see this more clearly. There is also the strong brown cast which is the shadow from the arm of the chair (the wooden frame is dark varnish). this looks definitely overdone in the jpeg version.
Lifting dark areasThere's not a lot of dark in these photos, but I found a small corner just to the left of the first crop area. Here is that area as it appears initially ( no processing on the jpeg, same tweaks as above on the raw). The crop here is tighter so these images are pixel for pixel.
Bringing back the highlights
up in the top left of the image theres an area with blown highlights - a bit beyond the depth of field, but we'll have look.
While a more detailed approach with photoshop might get back some of the damage to the colour areas, the areas that are flat white have gone forever, and with raw files these areas are always smaller - and with care when taking the photgraph, can easily be avoided or made insignificantly small.