I honestly don't have any good answers to your questions, I've just experienced better performance with Vulkan, but I'm sure someone here can give you a more technical answer.
And yes, the MMJ build is a tweaked version of Dolphin. I have both the official build and the MMJ installed and switch between them depending on games. Note that the MMJ build needs to be sideloaded to run.
And also make sure to use the official builds from the Dolphin website, and not from the Play Store as it is very outdated.
As for why the Shield doesn't run the emulator well, in terms of hardware I guess the CPU is the bottleneck.
However we've seen the chinese ports of Mario Galaxy and Twilight Princess run flawlessly so it should be possible!
Just "bad" optimization I guess?