It’s not clear to me what distinguishes, say, a document made with LaTeX from a document made in Word. So what’s the difference?
here’s a writeup: LaTeX vs. Word vs. Writer – things twice
the LaTeX document can be far more complex and customized. As you start to make complex equations (for instance) in LaTeX the document remains stable. Something that can’t be said for Word.
So whether to use LaTeX depends on the complexity of your document. For simple things, Word is OK.
LaTeX is a markup system for typesetting. The coding is universal and not dependent on proprietary software on your computer. It is easily composed and transportable.
Math. Latex handles formulas, proofs and theorems fantastically. I haven’t checked up on how Word has been handling that lately, but when I was writing my master’s thesis it was abysmal.
I’m a LaTeX fan, but take that article, and others like it, with a pinch of salt.
Many I’ve read have mixed up the capabilities of the fonts installed with the capabilities of the word processor. Proper small caps, ligatures, a real italic face, real bold face etc. are font features, and, as far as I know, Word can use these if they’re present. Whilst most versions of word have had Times New as the default font (is Calibra the new default?), there’s nothing stopping you installing e.g. Computer Modern unicode in order to access these features. On the other hand, OpenOffice.org Writer, last time I checked, doesn’t use these features: i.e. it won’t automatically insert an “fi” ligature, even if the glyph is present. This is probably one of the reasons why all documents created in OO.org look like a piece of shit.
What’s not disputed is LaTeX’s spacing is better. The LaTeX line spacing algorithm can be shown to be the best there is, for reducing the space wasted at the end of lines. Word uses an alternative, greedy algorithm, which doesn’t produce as nice a result.
Further, LaTeX handles typesetting mathematics very well. Somebody’s bound to point to the Word mathematics plugins, but all the ones that I’ve seen have been horrible, producing ghastly output.
Also, LaTeX markup is extensible in a way that word processors aren’t. If you need a new symbol, for example, a backwards “N” for some mathematics, and don’t want to create a new glyph, or something, then creating a new command to produce this is relatively easy.
Finally, the point of LaTeX us that content and styling are separated (like CSS and semantic HTML). You can write a document in LaTeX markup, then, after compiling with two different style files, have completely different looking documents (it doesn’t usually work as well as this, though).
Also, I’ve got to say, can you honestly not tell the difference between a document produced by LaTeX and one produced by Word/OpenOffice? To me, the difference is striking. Nearly everything about the LaTeX produced document is better: the quality of the default font, the spacing, etc. etc.!
Some journals will only accept articles written in LaTex, precisely because of the aforementioned stability, especially with math formulas. I’m writing quite a bit of LaTex right now, again because of the math angle. Word can use more than one math package, and I don’t know if all users will have them. Using LaTex guarantees that all parts of the article are in consistent format and readable.
I didn’t think LaTeX was a “program” as such - I thought it was just a system of mark-up that you can use in plain text files?
LaTeX is a markup, but to actually convert the markup into a PDF/Postrscript or DVI, you must run pdflatex or latex on the text file.
A historical note: I used LaTeX when I was in college, in the late 80s, to write professionally-typeset-looking papers, including math papers. I was working on old-style monochrome, text-based monitors, that wouldn’t show different fonts, formulas, etc., so using a modern-style word processor was out of the question.
Nowadays, modern Word and similar word processors are far more powerful, far more WYSIWYG, than anything that was available then, and with the help of Word’s Equation Editor or something similar, I can produce formulas that still don’t look as good as TeX’s but are pretty good for everyday use. So, while TeX nowadays has its advantages over something like Word, back when it was first introduced it really had its advantages.
Plus, TeX was written by Donald E. Knuth, who is a god among computer scientists.
In fact, he wrote it because he was unsatisfied with the typesetting for the second edition of The Art of Computer Programming. So he decided to take a few weeks to design a digital typesetting system, and managed to finish it in just under ten years. 
In addition to what’s been said above, one of the very nice things about LaTeX is that it produces nice-looking documents by default, rather than after you fiddle around with 100 different settings. The extensibility is the major selling point, though.
Also, there are WYSIWYG and other nice LaTeX editors these days, so you can reduce the learning curve to some degree.
Much of what I do is technical typing. I used LaTeX for a bit but found it difficult to collaborate unless you were careful that everyone had the same LaTeX add-ins. Also infrequently used “commands” were difficult to remember. I now use MathType and swear by it. It will output either LaTeX coding (error-free so far as I’ve found) or and OLS to input into Word or other programs. I no longer spend hours searching for where the freaking error or mismatched parentheses are in my LaTeX and can (using MathType’s easy to define keyboard shortcuts) touch type (no mouse usage) almost any equation symbol or structure I use with any frequency.
(Sorry to sound like a commercial.)
I’ve never used LaTeX, but I’ve used a lot of markup languages, starting with runoff and going through the Bell Labs packages troff and nroff and the macro package MM on top of them (customized for Bell System memos and reports.) The big advantage, beside equations, is the ability to precisely do formatting the exact way you want to, without the system guessing for you.
For a WYSIWYG formatter, I much preferred Framemaker over Word and OO, primarily because of its excellent paragraph definition facility. I did a large and complex user manual using it, and I seldom cursed at it.
LaTeX produces professional-quality output. Word doesn’t. It’s as simple as that.
Moreover, Word documents stop working once you have to share documents among people who aren’t running the same versions of the same software. LaTeX has been very stable for a long time now, and TeX has been stable for even longer.
Additionally, LaTeX comes with BibTeX, a package to handle citations and bibliographies in a standardized fashion. A lot of academics produce files that contain correct citations for all of their work in BibTeX format. All you have to do to use those citations, in whatever style you want (APA, MLA, even customized), is as simple as grabbing that file and writing a few lines of simple markup. Doing the equivalent in Word and Word-quality software would be mind-numbing tedious.
Finally, LaTeX works on every OS of even minor interest to modern academics. Word works on… what, is it up to two OSes now? And only on the latest versions of those OSes at that. Keeping up-to-date on OSes and computers is a worthless expense for most academics.
Use version control and add all custom style files to the directory.
The fact that you can use version control (in a useful way) on latex at all is IMO a major advantage. This is just one of the many advantages of having your source text be plain text. Another is that you can type a complete latex document on any computer, even if it doesn’t support latex at all (though I’m sure I’d make mistakes doing that, I’m also very sure I could correct them with fairly minimal work, using nothing more than Notepad and a latex processor if I had to).
Besides making equations look better, another benefit of LaTeX is that if you have 25 equations with the symbol phi in them, and if you later decide that you want to start denoting your parameter by theta instead of phi, you just do a search-and-replace.
In Word, if you want to change all phis to thetas in all the equations in your document, it would be hell.
Things I can do with LaTeX that I haven’t a clue how to with Word:
[ul][li]Incorporate massive amounts of dynamically generated information & graphics. It’s easy to modify a program or post-process to produce LaTeX for inclusion in a document.[/li][li]Automate inclusion of revision control & change documentation.[/li][li]Convert source documents directly to HTML and other formats.[/li][li]Dynamically cross-reference with section & page references.[/li][/ul]
I’m not claiming that these things can’t be done with Word, just that I don’t know how, and I’ve not encountered many Word documents produced by others that demonstrate that how to do these sorts of things is common knowledge among Word users.
And documents produced from LaTeX just look better, dammit.
When I last used LaTeX like 25 years ago, even then you could do stuff like search your document by font name, size, style, literally any characteristic of the text. I can only imagine it’s even more powerful now.