There are thousands of things you can do in a vectored art program you can't do in Photoshop, but if I had to pare it down to one single advantage over everything else, it would be the absolute editability of any object, at any time. Take, for example, gradients and blends. You create a gradient in Photoshop, it "sets" the pixels (paints them to a layer.) If you want to change the colors, you have to re-create it and replace the existing layer or put it in another layer.
In a vectored program, you can change colors, change end points, move end points, change gradient type, move it's center of origin, any number of modifications - all to the same object. The same is true of any object you create.
The largest advantage to using Illustrator, Freehand, or any vectored program is understanding the importance of vectored objects and their advantages over device-dependent raster files.
Wow! What a mouthful. :-) It's an easy concept to grasp. Raster (bitmap) images are pixel-by-pixel descriptions of an image. Output devices - monitors and printers- each require different quantities of pixels per unit to correctly render an image. I'm sure you're familiar with the complications of this, just try enlarging a 150 X 150 pixel image to 2000 X 2000 pixels.
For this reason, you require different files for each output device, making the image device-dependent.
Vectored art is nothing but a series of mathematic computations, and it's not drawn on the output device until run-time. So let's say I have a formula that defines a circle. In Photoshop, you have to create multiple files to display the circle correctly for various resolutions. But vectored art requires only one file - when a program goes to output it, it merely does all the rasterizing at output time.
Want to see an example? Open any PDF file in Photoshop. When it opens, it will ask what resolution you want. Set it at 72. Observe. Now re-open the file, set the res at 300. Note the differences.
What you have just done is allowed Photoshop, the output device, to rasterize the output of a vectored original (even though we've used a PDF instead of a pure vectored art).