Indeed, that makes a difference. I have been using pipe tables because they're easy to hand-code, and they seem to result in very narrow columns of equal width. With multiline or grid tables, when I place the resulting converted ICML in InDesign, it starts out with reasonable and differing column widths. Although they also seem to have the double tags on each cell.
With the Multiline table, the blank lines between rows seem to be captured as returns at the end of each cell.
I've also noticed that I need to check out the ICML file in order to change the table's format (eg, change column widths) in all cases. Which I didn't really expect, but now that I understand how it works, I can deal with it.