I also have this issue and notice in AGOL - depending on the scale, the polygon will be simplified to a degree. When we pull in the data to illustrator it pulls the simplified polygon at the scale it will fit within the artboard.
It doesn't matter if you up the DPI because it is still pulling the simplified polygon. Only when you zoom way into a feature does it draw without simplification... though this doesn't allow you to download all of the features in the project area.