A common misconception when buying copy paper is the idea that brightness and whiteness are really the same thing. There is a substantial difference between whiteness and brightness when using paper to print color, although there is a relationship between the two in reflectivity. The whiter the paper, the better it will display the printed color. Theoretically, absolutely white paper is 100% dazzling, and does not look white. Paper of this nature is impossible to achieve as it will reflect 100% of light shone and absorb 0% light.
Brightness has to do with the bleaching and fluorescing agents added to a paper to give the appearance of a dazzling white. If you hold such a white sheet under a black light, it will be brighter as compared to 100% cotton rag papers. Take a look at currency for an example. It does not fluoresce under a black light. That's how some people detect counterfeit bills.
In theory, the brighter and whiter the paper; the brighter and lighter the images will be. Colors on less bright papers are noticeably darker. For the most part, images on brighter white paper have more vibrant colors. However, some light colors in an image can appear washed out on the whitest papers.
To the naked eye individual white paper always appears white, but when placed side by side, various white papers show a range of color from a softer, warmer white to a very bright, cool white. The more blue light reflecting off the surface, the brighter and whiter the paper appears.
Another thing that we, as the consumer, have to keep in mind is that brightness scales can change from company to company and be subjective from observer to observer. In addition, there are other factors which could improve or compromise a paper's appearance. Rate of absorption, gloss, type of ink, and smoothness can affect the quality of the image in spite of it's brightness rating. Your best bet is to go by your own personal preference on how you want the image to appear on the paper, and how bright you want it to be.
At the end of the day, the choices of brightness and whiteness ratings are really a personal preference that will be related to the nature of the printing project, expected results, perceived results, and cost.