* Wget's the interactive, end-user tool, and my go-to if I just need to download a file. For that purpose, its defaults are more sane, its command line usage is more straightforward, its documentation is better-organized, and it can continue incomplete downloads, which curl can't.
* Curl's the developer tool-- it's what I'd use if I were building a shell script that needed to download. The command line tool is more unix-y by default (outputs to stdout) and it's more flexible in terms of options. It's also present by default on more systems-- of note, OSX ships curl but not wget out of the box. Its backing library (libcurl) is also pretty nifty, but not really relevant to this comparison.
This doesn't really need to be an "emacs vs. vim" or "tabs vs. spaces"-type dichotomy: wget and curl do different things well and there's no reason why both shouldn't coexist in one's workflow.