The advanced Brazilian Jiu-Jitsu student (brown and black belt) is proficient in a wide variety of material. And like a master's student in academic pursuits, is even more under the guidance of a mentor but will still find new material to pursue. The brown belt will know what a black belt knows, the rest of the game toward black belt is attaining proficiency and experience with the material.
It is common for students to take 350-450 hours at the brown belt rank. The live sparring aspect of BJJ becomes ever more prevalent to the advanced student as he or she attempts to refine strategy and read likely attack.
Brown belts are awarded to instructor peers. They are recognized for exceptional skills that are potentially challenging to everyone.
The best advice I can give after my 25 years of experience in this art is to not worry too much about time and expectations. What you should be doing is coming to class and absorbing material. You should never be concerned with grading your performance, nor adding up the hours in hopes of the calculations equaling skill. Come ready to simply play and have fun, everything else will fall into place.
It's natural to never feel ready for a rank change. Anything else would be unusual in the art. And that adage about needing 10,000 hours to become "genius" level in any art or study does have its detractors. One of the more serious arguments is that mentorship should be included as it's very easy to drill something wrong for years and achieve little "genius" level proficiency.