Or to make the question more clear - is the GRE significantly more difficult than the SAT, and if so then how? I've heard already that the verbal section has tougher passages and also vocabulary. And I've heard that the writing section is quite challenging. The math section is apparently supposed to be more similar to the SAT one than the other sections. Is this true about the GRE?

yes the GRE is a bit tougher.

the SAT is designed to assess high school students for college, while the GRE is to assess undergrads for work in grad school. inevitably, the gre will be harder because you are supposed to gain more knowledge throughout your academic career.

however, they sort of have the same logic, so if you did well on the SAT, if you study, you should do well for the GRE.

It's really not that much harder. However, there's more material, and the real key is that you are now being measured against all the other college grads in the country. And, fair or not, how well you do on the GRE has a lot to do with your college major.

Someone who was in the top 95% of the SAT may have gone to Harvard and studied Literature. When she's studying for the GRE, she realizes she hasn't touched math in 4 years. She's going up against engineers, mathematicians, and physicists (who, despite the stereotype, are often excellent writers). Those types have been trained to solve math problems quickly and concisely - they know how to approach the problems, not just the formulas and equations. She probably will not do as well against them in math, even though she probably scored much higher than they did onthe SAT 4 years ago. Consequetially, she will not score as high in the GRE precentile.

The opposite happened to me - I got in the top 72% on the SAT, but I went into engineering. Besides all the math, I also had to pass English, History, etc. When I graduated I was an excellent writer as well as problem solver. Even though I waited 6 years to take the GRE, I still got in the top 92%. 5 years after I graduated with an MS in engineering, I decided to go to business school. I took the GMAT (business school equivalent of the GRE) and with only 1 month of studying got in the top 94%.

The GRE isn't much harder than the SAT, just longer and more discriminating, and if you haven't touched math in 4 years, you will probably do worse than you did on the SAT.