CSS frameworks like Twitter's Bootstrap or Blueprint were created to help developers cut down on development time by creating preset definitions for all of the normal items found within the HTML markup of a website. In terms of the development of a website, having these items already predefined is a boon for many developers tired of having to rewrite the same chunks of CSS for multiple sites.
However, the usage of frameworks like these requires a buy in from not just your developers but from your designers as well. Since the framework is a predefined library, that means in order for it to be used most efficiently, your designers need to be creating designs that fit within the constraints of the framework. Both of the aforementioned frameworks rely on a grid model so it is no surprise that grid based designs are a much better fit for them. This does not mean that frameworks are not useful for site designs that do not fit the grid "mold" but it can mean that fitting the framework around the design can take longer just because the framework needs to be "stretched" to meet the new demands of the design.
All of that being said, which is the best approach?
As always, this is a choice best decided by looking at all of the factors. Is this a project that must be prototyped/completed quickly with a relatively modular/columnized design? If yes, then a CSS framework is probably your best bet. Is this a niche site with lots of outside the box design and isn't the most modular of sites? Then you're probably better off with "custom" css.