I think that while scalability, path operations, etc are true, they are somewhat trivial issues for most purposes. I do think there is a correct answer to this question.
The main benefit to using a vector program, such as Illustrator, is that the end product is a vector format: these vectors are all distinct and can be pulled apart, modified, deleted, etc. after the final product has been finished. That is, vectors are "open source", since they are freely and easily modifiable. Not so with bitmaps; after you've painted an object into a layer, you're not going to be able to delete that person from the layer, or tweak his body shape trivially.
This comes with its downsides: vectors are restricted to those operations that can be made to be open source. So some lossy operations, such as "blur this object and flatten it onto the page" are not possible with vectors. In fact, you will see that these lossy operations are precisely the operations that vector software don't offer. Thus, this is the fundamental difference between bitmap and vector programs. It is a tradeoff between power and modifiability.
As an example, think of a CAD program: if you want to adjust the width of some object (which will happen frequently), it would be best if adjusting the width was a single step and everything else adjusted itself instantly to accommodate this change. If this is to be possible, the kind of "bitmap" operations that Photoshop offers must be prohibited.
