If there is one thing that these two cameras can not be compared in is the price. Both of these cameras are dirty cheap for what they offer. Both of them provide excellent value for the money.
The lowest price Xiaomi YI I was able to find is around 67$ (here is a link to the store). On the other hand SJ4000 is a bit more expensive (best deal link here), but it comes with insane amount of additional accessories that are worth at least 30-35$.
Fake cameras on the market?
One major disadvantage of SJ4000 is that you have to pay close attention before the purchase and do the research, since there are tons of counterfeit SJ4000 cameras. Read this guide and learn how to know is the SJ4000 you are about to buy is fake or not.
On the other hand I still haven’t heard stories of fake Xiaomi YI cameras. I am not saying its possible, but its certainly not as common as it it is with its competitor.
Conclusion is, if you want to play it safe and do not want to do the research before buying, buy the Xiaomi YI.