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.