Most voted for AWPSs
Most web pages contain technical errors. The way web browsers deal with those errors is to guess what the author of the site actually meant. Most web browsers do this guesswork silently - they do not inform the user that they are guessing, let alone exactly what part of the web page they have guessed about.
Thus, on most web pages, what a browser shows is nothing more than a best guess - even though a web page may look 'right', it may very well be wrong.
The only way to make the Web a reliable source of information, is to ensure that there are no errors in web pages.
The WRI aims to improve accessibility and interoperability of the Web by improving the output of AWPSs (CMSs, blogs, forums, wikis, etc.). Given that more and more web sites are published through such systems, the idea is that if we can make those systems produce bettter output, web sites built with these systems will profit 'automagically'. Put simplified: "Fix one CMS, and all sites generated by it will be fixed".
W3C does excellent work standardising WWW techniques. However, defining standards is one thing. Getting people to respect/implement them is another. If developers don't follow, those standards will live in a vacuum while 'the real world' continues on its messy path.
Preaching to web designers to 'do things right' doesn't help all that much. Therefore, the WRI's approach will be more practical. The WRI wants to get its hands dirty - doing actual work on actual code to make AWPSs support those standards well.