Unfortunately I doubt anyone will point you to a resource that can do this.
First off, there are very few services that can give you an accurate representation of the links pointing to your site (you are however look at one site that can). Secondly, a link can be very hard to categorise because the site itself may not be in any particular category.
For example, I could have a webpage on my own site that I place links on as part of a link exchange. Then after 5 years, I've got so many that it becomes effectivley a directory.
A category for a type of link site is only a term given to it by humans in order to describe it. There is no semantic markup (none thats adhered to anyway) to describe the purpose of a site, be it directory, blog or otherwise.
Here's hoping that another mozzer proves me wrong, at which point I'll go and write an SEO tool that even Moz can't touch!