Most of the comparisons between these two that I've seen have been comparing performance at 4K. Obviously the Shield will be better in that case, but is it worth paying over twice the price for 1080p use?
Chromecast (Gen 1) has worked just fine up until now. YouTube stuttering has recently popped up, however, and the lack of a remote and Amazon Video is annoying for others when they try to watch something on my set.
Are there significant differences in casting (and emulator) performance between the two? Do either support playback of media from external hard drives?
I have two Mi Box's and for 1080p, they work as expected. I'm happy with them. Well worth the money I spent.
For 4k, it's a no brainer to get the shield.