I think a resume is more typesetting than word processing, so I would not use MS Word or OOo Writer. One could use Indesign or a free layout program.
Often resumes contain text in columns. Text in narrow columns is hard to wrap--TeX does a good job here. For even better justification use microtype with pdfLaTeX. I think with microtype the chance to avoid big gaps or lots of hyphenation is better than with word processors.
It's good if the resume matches the covering letter. Since LaTeX is great for letters, for example with the scrlttr2 class, it would naturally be a good choice for the resume.
There are specialized LaTeX classes. Though I prefer a class matching the class for the covering letter, such as scrartcl together with scrlttr2. tabularx does already good work then.
A resume can be used for many years in your working life, it will grow with the time. LaTeX is stable and remains mostly compatible, so you can reuse your resume when you apply for the next job in 10 years. Imagine, you would have used Works or Starwriter many years ago... you would require old software and an old operating system to reuse an old word processing document. With LaTeX it would be much easier.
ConTeXt, which is based on TeX, gives you even more control over typesetting.
On TeX tips, written by John D. Cook, I found a link where Dan McGee shares his experiences:
as is visible on the LaTeX project website. Moreover, your first slide could include the fundamental use of LaTeX (also from the above reference):
LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation. LaTeX is the de facto standard for the communication and publication of scientific documents. LaTeX is available as free software.
It is important to understand the idea of token lists, if you want
to gain a thorough understanding of TeX, and it is convenient to learn
the concept by thinking of TeX as if it were a living organism. The
individual lines of input in your files are seen only by TeX's "eyes"
and "mouth"; but after that text has been gobbled up, it is sent to
TeX's "stomach" in the form of a token list, and the digestive processes
that do the actual typesetting are based entirely on tokens. As far as the
stomach is concerned, the input flows in as a stream of tokens, somewhat
as if your TeX manuscript had been typed all on one extremely long line.