The advantages of LaTeX are that
It’s free.
It’s available for many machines.
LaTeX files are ASCII and are portable. Because they’re ASCII it’s easy to discover how someone achieved an effect.
You can use the editor of your choice (I sometimes use Word).
The typesetting’s better, especially the maths.
Style changes are neater in LaTeX. Style files for many periodicals exist. Many Word users don’t use styles or templates, and there’s a limit to what can be done.
LaTeX is extensible. If you want a new feature, you can look around for a free add-on or write one yourself. Pagemaker Additions and Quark Xtensions exist, but usually cost hundreds of pounds (the MathMagic QuarkXTension for writing maths and importing/exporting TeX docs costs over £600).
LaTeX’s floats are no more awkward than Word’s anchored frames, and the latter don’t always work well.
Disadvantages are
Font selection is difficult compared to selection in Word and Framemaker.
LaTeX’s not good at flowing text around pictures.
LaTeX encourages (almost insists on) structured writing and the separation of style from content. This is not the way that many people (especially non-programmers) are used to working.
Without a WYSIWYG front end, it’s not always easy to find out how to do things.