The primary advantages are its very small size and its tight integration with PostScript. The small size means that is very easily deployed (such as when you need something to generate documents); the tight integration with PostScript means that it is relatively easy (assuming you know a bit of PostScript) to augment the output with graphics (I have even, for example, sometimes used Lout to generate EPS diagrams to embed in LaTeX documents). Much easier than using Metafun, for example.
The main disadvantages are that it cannot do everything that the TeX engine does and that it has relatively few contributors.
For example, there's no way (other than manually inserting column breaks) to automatically generate balanced columns. And while non-rectangular paragraphs are possible in principle (such as for drop capitals or flowing text around images), this generally requires sacrificing hyphenation (and can be non-trivial for the non-expert user).
Lout also has fewer people contributing to/using it, so it does not have the rich ecosystem of TeX and friends (e.g., while you can use it to generate slides, there are more and more powerful LaTeX styles available). Integration with bibliography tools and sites (that generally expect/produce BibTeX format) can be another matter.
With respect to typesetting quality, it uses the same line-breaking algorithm as standard TeX; it does not have the microtypography features of pdfTeX. For typesetting anything mathematics (beyond basic math), TeX is generally superior (which should not be surprising, given the effort Knuth put into getting that right).
Also, while modifying/creating LaTeX packages these days is not exactly child's play, Lout poses some challenges of its own; its functional typesetting language (used both to describe the content and how that content is laid out via so-called galleys) can be difficult to grasp for a novice.