My answer to this question would depend on what kind of free web site you are planning to build. If what you want is a private site for your organizational use where you can control who gets access privileges to users of the web site, then Google sites will be the ideal place to build your web site.
If you intend to make money on your free web site and would like as much traffic as possible, then what you are looking at is a public site that you can monetize and the better place to build your site will be at Blogger.
Blogger is the better site to park your free personal web site if you want maximum exposure to everyone in the world. I have web sites at both Blogger and Google Sites and apparently, Google Sites is not indexed very well by the Google search engine, not as well as Blogger anyway. I sometimes have to put links to my pages at Google Sites on my web pages at my Blogger blog just so that the Google search engine will be able to index my Google Sites pages.
One advantage of Google sites is that authorized collaborators can upload documents as attachments to the information contained on a page. This can be extremely useful for team members who are collaborating on the implementation of organizational programs or projects. For instance, you can prepare a report on the progress of your work and upload it as an attachment which anyone allowed can view.
Another advantage of the Google Sites web page is that you can embed sound files on the web page using an mp3 player widget. Blogger does not provide a built in tool that can be used to play mp3 files on the blog page. You can only embed pictures and videos on a Blogger web page as compared with pictures, sound files and videos for the Google Sites web page.
One difference between the two free site-building places is the degree to which HTML editing is allowed. Blogger gives considerably more leeway into how far the user can edit the HTML behind the formatting of his blog. However, the only thing that you can add are codes that will be applicable to all blog posts because the HTML actually contains template codes for formatting all the pages in your blog.
There are, moreover, a lot of free Blogger templates that can be used by searching the Internet. The only requirement is that the link back to the web site of the template creator is not removed from the template. To use your own template, you have to copy and paste the HTML and CSS codes into the HTML window provided for this purpose.
Google Sites on the other hand provides very limited HTML editing and it focuses only on the content of the web page. However, there is a lot of templates to choose from and the templates are much newer and better looking than the Blogger templates. You can also create two-column pages that look very much the same as the pages of a magazine. This can make your text a lot easier to read so if your page contains a lot of text, you may use multi-column formatting feature of Google Sites.
If what you need is a central place where you can have a readily accessible place to store information for an organizational program or project, your free personal web site would best be built at Google Sites. However, if what you plan is a money-making web site that can have a maximum exposure and generate a lot of traffic, then you will be better off at building your free personal web site at Blogger.
Read my other article on creating free personal web sites at Google Sites and WordPress at: http://publishtoweb.blogspot.com/2009/12/creating-free-personal-website-at.html.