You can open an Illustrator file in Photoshop, which rasterizes it into pixels with beautiful results. So why would you want to Export it instead?
Exporting offers a lot more options to make your Illustrator art far more usable and editable within your Photoshop image. To see what I mean, open an existing Illustrator document that contains Layers, Text, and Transparency (or create a new document using these features). Now go to File > Export and choose Photoshop (PSD) as the Format. In the Photoshop Export Options window that opens, the advantages of Exporting become obvious. You can choose to maintain your Layers in the PSD with Maximum Editablity, and Editable Text. When you open the Exported PSD in Photoshop, the advantages of Exporting grow. Not only do you have Layer Groups with the same names as your Illustrator Layers, but Sublayers containing individual objects, plus adjustable Transparency, and Live Text. With advantages like these, if I need to convert vector into pixels, I always choose Export.
Tip provided by Jeff Witchel, Certified Adobe® Training Provider.