I’ll add three points:

1) Another huge advantage of LyX is integration with BibTeX for citations and bibliographies. This is something that does not exist for free, in a form useful for professionals and academics, in the Microsoft Word world. There, you have to pay good money for a system like Endnote that locks you in even worse than Word does — your documents simply won’t show any citations unless you have Endnote installed!

LyX + a BibTeX reference manager (I like JabRef) = freedom from Word + Endnote.

2) LaTeX produces higher quality printouts because it’s not limited by WYSIWYG. Screen fonts are an order of magnitude smaller in resolution, so if you want something to look identically on screen and on paper, you will have to adhere to the screen’s lowest common denominator. In fact, it’s so poor that many printing features, such as font kerning, aren’t even bothered with in the WYSIWYG world.

I can spot a printed Word document from across the room. A LaTeX document is indistinguishable from a book — in fact, many books you own were probably typeset in TeX.

3) To be fair, Word has incorporated some post-WYSIWYG thinking. WYSIWYG was terrific for the office letter environment — a secretary could quickly produce a letter and send it to the printers while being able to proof-read it on-screen. But, with longer things, like technical documentation, it presented problems. Re-formatting was a nightmare of meticulous work. So, Word introduced “styles” — which is really a WYSIWYM concept. You can set your “style” to heading without worrying to much about how it looks. You “mean” it to be a heading, and you can format it when you’re done writing.

To an extent, Word does a better job than LyX in letting you change the formatting of your document. LyX lets you change things like margins, fonts and spacing, but the need to preview as PDF makes it slower to tweak.

I hope this will get better in future versions of LyX. Live PDF previewing, perhaps?