When done right WordPress Categories can rank in Google as you can see in the screenshot.
I tend to use Categories as my main archives others use Tags, some use both. SEO wise there’s not much difference between them (the HTML output is the same), what I would avoid is a duplication of the same content through both sets. You wouldn’t generally create two Categories/Tags with the same content since it adds no SEO value.
A site about WordPress for example could have Categories and or Tags about each version of WordPress, WordPress 4.0, WordPress 4.1, WordPress 4.2 and all versions in between. Many site owners see Categories as their main archives, maybe a Category called “WordPress” and an almost free for all on the Tags with Tags, “WordPress 4.0”, “WordPress 4.1”, “WordPress 4.2” and all the versions in between and will link anything related to WordPress into the Category “WordPress” and all the above Tags.
The problem with this is the content (the Posts) that are listed in these Categories and Tags can be almost identical, the page you are reading now would fit in all the Categories and Tags I listed above and so would most of the posts on this site. This means on archive pages with this sort of setup the tags and categories are not unique, the only real difference is the name of the Categories/Tags and Google is smart enough to know this and will tend to consider some of the Categories/Tags duplicate and won’t index them.
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