In most of my web site I have a lot of external links to my other sites and other external sites.
I need to know when is better to use rel="nofollow" or rel="external" in a website?
You may use external for every link to a different website, no matter if it’s yours or not, if it’s on the same host or not.
You may use nofollow for every link that you don’t endorse (for example: search engines shouldn’t assume that it’s a relevant link and should not give any ranking credit to this link).
You may use both values for the same link:
<a href="http://example.com/" rel="external nofollow">Foobar</a>
Note that external doesn’t convey that the link should be opened in a new window.
Note that search engine bots (that support nofollow) might still follow a nofollow link (it doesn’t forbid to follow it). FWIW, there is also the nofollow value for the meta-robots keyword (which may mean the same … or not, depending on which definition you follow).