Relative Divs
Pros-First they allow for your site to handle a change in content. IF you were to use all absolute div tags you could easily have your tags overlap and hide each other when the data within them changed. Secondly, many good sites allow for the information to wrap depending on the screen resolution and browser size that a user uses to access the web page.
Cons-Slight changes in the size of your relative divs can cause your tags to change how they wrap. Also, change in information can sometimes cause frustrating changes in your overall site look, which in turn requires some tweaking.
Absolute Divs
Pros-First they solve the issue of having a small amount of content scattered across a larger area. This is usually the case with header data or heavily graphical sites. Sometimes you will have a large area with a background image and you will have few controls along the edges and in the middle that need to be placed exactly. Relative divs would be a headache in this case as you would need multiple extra divs and they would easily break when a user resized their browser or access the site from a small resolution screen. The other major use for Absolute divs is pushing content out of the area it was originally in. A great example of this is menus! The header of a menu is usually contained within one div but the items within it fall into another div when the menu header is hovered over. Also, tooltips and things that popup on the screen usually require absolute positioning.
Cons-Absolute divs run into a similar issue as Relative ones if they are used incorrectly. The issue is they become tedious to manage. Specifically, if you used 10 absolute divs to control your content areas and one of those areas became larger or smaller because your content changed you could have to modify the location of every single div. Which would take a great deal of time.
In Conclusion - Many times you will want to use a site with Absolute and Relative div sections not only because they both serve a purpose but because when using them together you can create the best looking web pages with the least amount of time and code.