I prefer Textile because I find the linking syntax to be much more intuitive (I can never remember what's in parens and what's in brackets in Markdown).
[Hacker News][hn] is a website.
[hn]: http://news.ycombinator.com/
You should generally use these all the time when writing documents you intend to maintain. For quick one-offs like blog comments, you can instead use:
[Hacker News](http://news.ycombinator.com/) is a website.
Once you actually use markdown for non-trivial documents, it is very easy to remember its syntax.
"Foo Bar":http://foo.com/bar.
is ambiguous, and the result depends on the parser. It could end up as <a href="http://foo.com/bar">Foo Bar</a>.
or it could end up as <a href="http://foo.com/bar.">Foo Bar</a>
The former is probably what you mean most of the time, but then there's no way to link to the (valid!) URL "http://foo.com/bar.".So while I use Markdown, I recommend Textile just so you can avoid this issue.