This is why the A6000 was close to the FF camera and why when you look at all the measurements (take an average to be fair) the E-M1 performs better than expected compared to the A6000.
For the avoidance of doubt, when you say "better than expected compare to" you mean "worse than, but not as bad as expected compared to", right?
No, for example, at ISO 120 and 200 the E-M1 would have more DR, or when using the same DOF it would not be "worse" at even more ISOs. It simply depends. This is the topic. When considering DoF, smaller sensors often perform a bit better than larger ones. Not always, but pretty often.
Let's stick to the same brand here so no one can get us off topic and turn it in to bashing as then tend to do.
So take the A6000 and see how it performs favorably against the new A7ii. Both have the latest sensors. If you account for DoF, the A6000 beats the A7ii at almost every ISO. If you prefer more DOF, the A6000 is the better option.