The problem is you are going from a full color image (JPG), to a limited palette image (GIF).
That conversion needs a lot of work on IM's part to do a 'reasonable' job. That is read all the colors, reduce the number of colors to 256, recolor the image to use just those colors, in a way that visually simulates the larger variety of the original image.
The steps are looked at in detail in IM Examples, Quantization and Dithering
http://www.imagemagick.org/Usage/quantize/
and it is NOT a simple task, and even has a lot of options and methods that can improve things.
For GIF animations dithering individual images separately also produces extra problems of 'dither noise'!
see Video to GIF for a step-by-step guide...
http://www.imagemagick.org/Usage/video/#gif
From the look of these images, I would actually suggest a re-think on how you are generating the images!
The static frame in the middle can be dithered separately so that any dither noise remains static.
the outside frame can be drawn with limited colors and less gradient use, better suited to GIF images.
Does it have to be GIF? what is the final display mode?
A desktop digital frame could probably avoid the need for limit GIF all together.
A web page can use a java to cycle between the JPEG/PNG frames, to animate and again avoid GIF.
Finally the middle is not animated. You could split the animation into three parts. Left animations, static middle, right animation. That will reduce the complexity and let each part deal with the GIF limitations separately...
Also means you only need to generate the static middle (as a higher quality JPEG) for different images.
See splitting an animation
http://www.imagemagick.org/Usage/anim_mods/#split
PS: nice image of the Great Wall! I have a few myself, though I have not used them online, yet.