Conversion from RGB to CMYK Color Shift

I have had this question for several years and never got around to asking it.

I am very familiar with converting RGB files to CMYK in Photoshop. I expect some duller color shift when I do this to the smaller CMYK gamut. Usually it is not a major issue. With Illustrator it is different.

As an example, today I receive a .AI Stock image from a client to convert to CMYK. It was a multi-colored vibrant abstract background with gradients that I knew by looking at it that the CMYK conversion would be obviously apparent. When I switched the document in AI to CMYK the image was not even close and half the colors blew out to white or black! Unuseable for print. (I have seen this many times on stock vector background files in AI). 

As a "test", I copied the AI RGB file and pasted it into a Photoshop Adobe RGB document, On-screen the AI file matched the PSD file side-by-side (so far). In Photoshop, I went to Mode>CMYK and the colors "slightly" shifted to a less saturated version (as expected), but totally usable for print (perceptually the same for most people without placing next to an RGB screen version)..

So why do Illustrator and Photoshop yield such "radically" different results on the same file.... I mean RADICAL!

I have seen this behavior on many Stock vector files in AI - I just usually give up and move them to Photoshop to make predictable CMYK conversions. I am assuming I have some default setting or behavior configured wrong in Illustrator? Or is this normal?