Indeed. Thing is computer graphics is a parallel invention. Today you can see two distinct groups of graphics programmers. The other builds on a tradition from GUI programming, this group is heavily entrenched in 2D graphics. For their merit they did use their brightest people to solve the color reproduction problem that is actually a insanely complicated issue.
The second group comes from a very academic background that actually tried to tackle 3D graphics and motion graphics. This group of people had a much more challenging task and actually needed to do much more thinking about how to approach their work. This group has a totally different take on how anti aliasing works.
Since AE is strongly affected by the later culture its not surprising that their rendering engine is more sophisticated. See most of the glitches and rendering errors exhibited by main line 2D rasterizer (Including one in chrome, safari, ie, QT and firefox) have already been solved in 1990s. One quite pronounced problem is that quite many 2D programmers seem to think that box filtering is actually a good strategy. And many systems even today do not account for the screen non linearity in the internal calculation.
We can do better? Or then not. Signal processing theory tells us that we have a choice between ringing and blurring. It is clear that you prefer blurring but that does not mean its a universally true preference. Personally I prefer the look produced by a Lanczos filter, but many people find it disturbing. This is also the reason why illustrator is so sharp, see for text the sharpness is more important than anything else, since graphics designing is much about text it makes some sense to do this.
Ok, so back to the question what can you do? Well you can render outside illustrator, but then you get no feedback on screen. There is also a bit of a curious development in Illustrator itself. See it has 3 different ways to render the picture. Hinted render (that you despise), art optimized (That uses 4x4 box filter non corrected) and a openGL render.
Now the openGL renderer is actually better that the 2 other options, because 3D accelerator programmers represent the other category and hardware manufacturers handle some of the things for you. Only adobe has forgotten to actually implement a save routine that uses this renderer. It has many advantages, including the fact that it fixes many of the traditional render bugs associated with vector engines. Presumably a few versions from now as aside effect this will be fixed. You can however improve the art optimized by using a linear working space and then enabling color correction go convert that to sRGB this makes the image much better. It still has 4x4 levels of alpha but its now distributed better so results are where it counts more. Also you can aa twice with are optimized as a rasterization effect on the layer at extra size then a second time down sampled.