Meta tag vs robots.txt

There is one significant difference. According to Google they will still index a page behind a robots.txt DENY, if the page is linked to via another site.

However, they will not if they see a metatag:

While Google won't crawl or index the content blocked by robots.txt, we might still find and index a disallowed URL from other places on the web. As a result, the URL address and, potentially, other publicly available information such as anchor text in links to the site can still appear in Google search results. You can stop your URL from appearing in Google Search results completely by using other URL blocking methods, such as password-protecting the files on your server or using the noindex meta tag or response header.

Both are supported by all crawlers which respect webmasters wishes. Not all do, but against them neither technique is sufficient.

You can use robots.txt rules for general things, like disallow whole sections of your site. If you say Disallow: /family then all links starting with /family are not indexed by a crawler.

Meta tag can be used to disallow a single page. Pages disallowed by meta tags do not affect sub pages in the page hierarchy. If you have meta disallow tag on /work, it does not prevent a crawler from accessing /work/my-publications if there is a link to it on an allowed page.