I’ve read articles applauding the pixel preview functionality of AI, especially when it comes to designing icons. While it does a good job for higher resolutions, I wouldn’t use it for 32×32 and below. Compare these two icons:

Both are 16×16 pixel circles drawn with vectors, and snapped to a 1×1 pixel grid. You can hover over to see which was done in Illustrator and which in Photoshop, but first decide which one looks better-rounder, sharper, use whatever criteria you want.

IMHO, the Photoshop one is better. It’s not quite as crisp, but it seems rounder. The Illustrator one looks boxy and uneven.

Here’s a 1600% zoom in on both icons:

Illustrator, zoomed to 1600%

Photoshop, zoomed to 1600%

Note how Illustrator adds grey pixels to the left and top of the icon. It’s got to be a bug in the software. I had been considering using Illustrator for low-res icons, but based on that finding, I’ll stick with Photoshop.