In terms of academic careers, does the department type matter between Computer Science, Engineering, or Information?
My short answer is that if you're staying in academia, it probably doesn't matter much at all. If you're considering leaving, then CS > "Engineering" > IS (for many tech companies, at least), to a mild-to-moderate extent.

My longer answer is that it depends how you sell yourself. The material you learn will likely be very similar, but different communities will focus on different aspects of HCI. This will probably be most evident in the research coming out of each group. To that extent, I recommend taking a good look at the research coming out of each program. The focus of the researchers will give you a good idea about the differences between the programs.