LaTeX agrees very well with people who are used to deal with abstract concepts. You don't see the final result when you write a document, but rather describe the document structure – not the formatting itself – in a markup language. A program, a compiler if you want, then transforms this document structure into a formatted document.
For people who have programming experience or who work with markup languages like HTML it is very easy to learn. For those people it gives publications of professional quality much quicker and easier than Word right from the beginning. For others it may take a bit longer to get accustomed to the concept. Most people that I know get better results with less time and effort once they have learned some basic principles of LaTeX.
LaTeX is based on a plain text format. That means everything that influences how your document is formatted is directly visible and editable as text. There are no hidden properties or nested menus, just plain text. You can often copy and paste some example for a more involved formatting from somewhere, play with it, and see what it does. Bit by bit you expand your "personal library" of code examples and older documents that you wrote and learn to solve problems quicker and quicker.
The layout and typesetting of documents that are formatted with LaTeX are of very high quality. It is nowadays possible, but difficult to achieve such quality with word processors. Not too long ago it was simply impossible. LaTeX is also very stable and reliable software. The base of LaTeX, TeX, can be considered 100% bug-free. LaTeX runs on many platforms, including Windows, Linux and OS X.
LaTeX is furthermore free software, that means it is free to download and install, and you can even obtain, modify and republish the source code under certain terms and conditions. People can implement features that they need and then publish the changes for everybody to use. A huge number of packages for diverse purposes is available for download from a central repository, CTAN, and is packaged in free LaTeX distributions like Texlive.
This means you can do a lot of things in one document without paying anything or even installing third-party software. And if you give a document that needs a certain package installed to someone, this person can simply download and install that package without hassle. This contrasts to Word, where certain features, like reference management, depend on commercial software like Endnote. You are also very flexible how you set up your working environment. You can use your favourite text editor, your favourite program to generate graphics and your favourite reference manager (as long as it supports BibTeX).
In conclusion, I think that LaTeX is ideal for scientific literature like articles or books. Word processors are better to write letters or memos that are not to be widely published, generally for "quick and dirty" jobs.