Google Sites and Blogger are both owned by Google. Originally, Blogger was the best Google service for blogging and Google Sites was the best service for making websites. Keep in mind that blogs and websites used to be more separate as entities back when these services were created then as they are today.
WordPress used to lead the Blogging CMS industry. WordPress soon evolved the ability to create static looking type website in addition to keeping their blog characteristics. Other blogging platforms, including Blogger did the same to stay competitive. When Blogger inherited the ability to be a blog or a website, it started to make Google Sites obsolete.
Both Blogger and Google Sites allow integration with other Google Products through gadgets, but Blogger seems slightly more compatible. For example, when you create a Google Reader account or a FeedBurner account, you see Blogger integration options, but nothing in regard to Google Sites. Perhaps Google knows Blogger is the future and Google Sites isn't. Maybe the sheer number of Blogger users demands more compatibility contrary to the lesser number of Google Sites users.
While Google Sites still allows for more control as far as design then Blogger, but Blogger's offer more templates to choose from. Not to mention Google Sites template are horrid and not even web 2.0 looking... The Blogger templates are as professional looking as they come.
As the web grows, building a website isn't a make or break factor anymore, but generating web traffic is. Blogs are the only legal, and effective way to generate website traffic today, making blogs a must for any modern website. Blogs are extremely important today, and Blogger is a much better blog then Google Sites.
Without a doubt, Blogger is a better website or blog solution than Google Sites.
Rest in piece Google Sites.
You might consider the Affordable Website Package as a means to create a website. The package includes a WordPress website, web hosting, a custom logo, an email list, SEO and continual support.