The GFDL was written with books or multi-page documents in mind. It contains many provisions that are cumbersome for non-written works or short written works. It is historically relevant because it is a non-software copyleft license that predates the Creative Commons Share Alice license.
In nearly all circumstances you will want to choose the CC-BY-SA license over the GFDL: the license is more widely understood, compliance is easier, and (in CC 4.0) it accounts for newer developments like database rights. I could only see the GFDL being preferable if that would allow a user to lawyer around some details of the CC licenses, or if you're actually dealing with a book.
A big difference between CC and GFDL is that GFDL requires all copies to accompanied by a license statement and the full terms of the license. That's practically impossible for images. In contrast, CC allows a link to the full text, an in many cases just the note “CC-BY-SA 3.0” would be sufficient. The GFDL also allows some sections of the document to be marked as invariant, they must be produced verbatim in derived works.
Note that Wikipedia's licensing is a bit more complex. They do use GFDL/CC-BY-SA dual licensing for most text contributions, but should be treated as purely CC-BY-SA licensed by downstream users. Individual pages may contain non-GFDL content. Media files have their own licenses that are noted on the media file's page. Note that the GFDL 1.3 contains an explicit compatibility clause that allowed Wikipedia to relicense their GFDL content to CC-BY-SA in 2009 (but it was scoped to prevent further relicensing).