EE is more geared toward theory and IC level design, EET is more hands on and geared toward board level design. In the job market, the two degrees are mostly interchangable unless you get into ultra high tech stuff. The main difference I see is that EET students spend A LOT of time doing lab work and learning how to use test equipment, whereas EE students don't do very much lab work at all.
There are of course differing opinions on who is better prepared right out of school. My experience is most EE's don't know how to use much equipment right out of school, but are much better at the "math" end of things. I knew more about how to design simple circuits as a tech then many BSEE's I used to work with. (I can hear the wailing and gnashing of teeth now )
Example: Purdue EE's work on things like carbon nanotubes, EET's design and build amplifier circuits, controllers, program PLC's, troubleshoot circuits etc.....
I have already been through differential equations, and found them easier to understand than integration...go figure. I got my A's and B's in my Calc courses...I just have to be able to apply it in every course from now on. RF (communications) uses a lot of it.
So what is a "computer engineer"? Software or hardware? Network design? There is an option for EET at Purdue called CPET which is Computer Programming Engineering Technology that is mostly a few extra structured programming classes and some networking courses.