The Shield looks realistic and great. The chromecast looks absolutely terrible.
Both Devices have the EXACT same settings, including on the TV, so why does the SHIELD look so awful compared to the Chromecast?
Are they on different HDMI ports?
Contact Nvidia support, when I contacted them they were very helpful and sent me a new device even after **I broke it. ** In the meantime if you go to settings, then device preferences > display & sound > Advanced display settings, is your dynamic range on full? If so next go to custom display mode then go to the bottom and try different display configs to see if the issue persists. Try RGB 8 bit, YUV 422 & YUV 444. It seems like it could be color space issue. Also is your TV HDR capable? Are you able to turn it off for that specific hdmi port that the shield uses?
edited out: Think 2 looks ok
The Chromecast looks over-saturated to me.