advantages of mindmapping
The most obvious advantage is you can see all the information on one page. No more shuffling. Try to get the major headings in an eight page outline. No contest.
The less obvious advantages require digging a little more. There are many mindmapping concepts critical to maximizing performance that many "mindmappers" aren't aware of. Reading any of Tony Buzan's work, especially "The Mind Map Book" will clear it up. Real mindmapping uses colors, images, key words (not phrases or sentences), and arrows.
Many functional features add additional value. You can insert new ideas easily. Try to write in 5 new points under I.A.1 in an outline printout. Add a new empty branch to signal incompletion and a question to be asked. Reducing detail simply involves lopping off the outside branches.
Also, they can be used to take notes, make speeches, teach, learn, test, and organize in ways that simple outlines just can't compete with. Try building an outline in random fashion, they way the thoughts occur to you in a brainstorming session. With a mind map, you can jump from side to side with no penalty.
My advice. Grab your favorite/most recent outline, convert it to a mind map (or "business map" if the term bugs you), and see what you think. Make sure you use color, doodles, arrows, and key words only. See which one sticks in your mind better. Try to present each. Try to modify each with a pen while you are waiting your turn to speak. If you still don't see the point, then just go back to your comfort zone shaking your head at all the strange people out there who use these funny-looking notes.