I use InDesign almost exclusively for print layout but there are two things I still use Publisher for.
One is mail merge. I realize InDesign can do data merge, but it creates a new page for each record. It is cumbersome to work with really really big databases. With Publisher I just print my one-page document, and the software does all the work. Is there a way to do this in InDesign?
The other thing I use Publisher for is business cards, since Publisher will automatically tile my business card on the printed page, with crop marks. I could use Step and Repeat, or export to PDF and place the PDFs on a new page, but these require many more steps.
In almost every other way, InDesign beats Publisher - in my specific case, primarily due to its image handling and better respect for CMYK numbers.