Let's say I put the following two datasets in the best possible model (same model for both):
Could the difference between both AUCs be high? How much?
Yes, the performance can vary a lot using feature engineering.
Example: suppose a dataset where the response variable $y$ is true if $x$ is odd.
x y 346 F 13 T 178 F 64 F 987 T ... Most learning models will fail to identify the pattern and will perform poorly, usually falling back to always predicting the majority class. However simply adding a feature $x \% 2$ to the data will allow any model to perform perfectly.
Of course this a toy example, but the point is that a single well chosen feature can drastically change the performance. Naturally the increase in performance totally depends on the data and the nature of the features added.
I would say that the best possible model for the raw data would derive all the meaningful features that you would have created from the data anyway.
And I would say that the best possible model for the feature-engineered model will remove/ignore unnecessary features.
The best possible model would have AUC of 1 anyway. It makes all predictions correctly.
But even in the context of noise where AUC of 1 can not be achieved, I think the argument holds.
But learning rate/convergence speed may vary.
