To me, there is a clear visual difference between the jpg and gif that you posted... the jpg has much smoother color transitions, and doesn't look "grainy" like the gif. Especially in the pouch... when I looked at your first photo, I was immediately aware that it was a .gif rather than a jpg, which is of course why I mentioned it. For me, that would be the major reason to use jpg instead of gif... gifs can use a about 256 colors, whereas jpgs can use millions.
There's also the size issue. Especially for larger images, jpgs (if optimized) are much smaller than gifs, in my experience. For example, the .gif image that you posted is over 100k. The jpg (which I optimized in photoshop) is of superior visual quality (I think) and is only a quarter of that size :
Let me know if I need to go into more specific details here.