By CE I will assume that you mean Computer Engineering (which Pitt refers to as CoE so as not to confuse it with CivE and ChemE) and attempt to answer your question.
Where as EEs often deal with large (physically big) circuits including those that run industrial motors and with numerous analog systems, a CoE deals more often with smaller (physically) circuits and almost entirely digital systems these days.
We design the digital logic that things like microprocessors use in order to execute instructions, the pipelines the caches, the memory modules the flow of ones and zeros through the ALU (which we also design) into registers and such, then we deal with the placement of the microscopic transistors that make all this stuff become a physical chip that you can hold in your hand.
In some cases there are pre-fab parts that we work with in order to create a new device, such as taking existing things like processors and flash memory and turning it into a portable device that plays mp3 CDs. It’s not really much of a lego method, since there’s research to do, plans to draw, changes to make, testing that has to occur, measurements to be taken, etc. before the prototype ever really happens.
Granted there is quite a bit of overlap between EE and CoE, at least in the early stages of becoming one, until you get to the point of specializations. EEs did not have to deal with designing a CPU chip, and CoEs didn’t learn to work with ladder logic diagrams or high voltage systems. We pack it into a quarter inch square and run it with +3.3VDC and they make it fill a factory and run on 480VAC.
The math requirements were the same, the physics requirements were the same, we took the same circuits courses and our departments shared the third floor of Benedum Hall. The majors were so similar that the College of Engineering at U Pitt would not allow an EE to take a CoE minor, or a CoE to take an EE minor because technically you could’ve had one anyway with the classes that were already dual-CRN (meaning they had a registration number out of two deparments and could be referred to as say, EE1185 and CoE1185).
So they’re the same, but different.