Mritty gives a pretty good answer. I’m comp.sci myself, but i wouldn’t say i look down on the IT-crowd or the hardware people, we all do different things that are all needed.
IT-stuff is everything like some coding software, databases, designing GUIs, managing IT-projects, understanding internet routing and such. It’s basically the “social science equivalent” of computer science, or the “softer” stuff.
Electro engineering is the circuitry underlying all the computers, the low level stuff is resistors and circuitry, and lot’s of physics, semiconductors. When you go more advanced you get a tad more math than either IT or comp.sci, so you may be more fit for tasks such as signals engineering, specialized hardware engineering, circuit design, or anything which demands more proficiency in math or physics. It’s basically the nitty gritty of getting dug down into the pure details of the underlying electronics. If you choose to go even deeper an electrical engineer can almost turn into a physicist. This is the “harder” stuff.
Comp.sci is in between electrical engineering and IT. We get some of the IT stuff and some of the electrical stuff (but not that much). We also have areas which are considered mainly computer science, for example advanced algorithm design (how to solve problems efficiently with a computer), parallell processing, cryptology, logic but we do a fair amount of coding and also learn about IT-projects, and methods for developing of advanced software as well. I would probably say we get the most coding time out of all the branches, although i know IT gets alot as well. We also get a tad of the hardware stuff.
I chose comp.sci because i am not a hardware geek and i find the low level electronics stuff boring. I could probably have become an IT-major, because i like some of the softer stuff with building GUIs and usable apps easily, but at the time i was starting the IT-field felt too young, and overhyped. By today it has matured somewhat.
I wanted a good, usable all round education in computers, so i chose comp.sci.
There are ofcourse many overlaps between all three of these fields, and if you start in one of them usually you can do your masters in one of the others if you find that more interesting down the road.