Let illustrator means that you use the Colour Settings files colour management. Usulally this is the CMYK workingspace and possibly converting from document CMYK to the output devices ICC profile.
Letting postscrip determine colours you include the simplified colour management built into postscript, can't remember the name of the file but it builds on look up tables and was one of many colour management systems that no longer are in use with the standardised implementation of ICC profiles. On a non Adobe printer this means you cannot access blackpoint compensation.