Well...the purpose of the FE exam (8 hour state exam)...is to qualify you for the PE exam. (8 hour state exam)
PE stands for professional engineer. When you graduate with a bachelors in EE...you are really not even allowed to call yourself an engineer...you simply have a bachelors degree in in engineering.
Some jobs want you to be a PE. If you look closely, many say P.E.'s preffered.
Personally, I did not take the FE in college. I actually waited 7 years out of college to take it. I landed a new job and they were all over me saying..."what do you mean you don't have your PE...why not?". So I said...ok, I'll take it.
The FE covers roughly the 12 different phases of engineering...and it basically verifies that you actually learned something in college.
Being out of college so long, I studied for 6 months...roughly about 250 hours of review. They make a great review book btw. The test is 8 hours long...turned out I passed it.
Since I had 4 years experience in the engineering field (required), I decided to take the PE right after it. The PE covers your specific discipline...electrical for example in my and your case. I had taken the afternoon electrical for the FE...so I was already kind of hot on electrical...and studying. I studied for about 3 months for the PE...roughly 150 hours and passed it first shot. So now I am state certified and I get the little letters after my name on my business card...and on my resume. John Smith, P.E. for example.
Can an engineer be great without a PE? Absolutely.
Can an engineer be lousy with a PE? Absolutely.
For the most part, having a PE is a good thing. It's kinda like the bar exam for lawyers and the CPA exam for accountants.
Click on this link...should have lots of additional information.
http://www.ncees.org/Exams.php
To answer your question why some degrees require it and some don't...not sure.
I'm an EE and my current company sure wanted me to get it. And yes, upon passing the PE I received an insta-raise right on the spot. My company can bill more for me and they have higher credentials...along with myself.
And yes, both tests are considered very difficult.
I would suggest taking the FE now...but as you can see...it might not matter. If you have a wife and kids...your odds of passing go down considerably due to time restraints. Best to do when single and fancy free.