If you set up a job with an extended-choice-parameter which simply echoes the value of the parameter, and call it directly from the Jenkins UI, the parameter is correct.
If you call the same thing using a URL request, that parameter is blank, both in the parameters when you look at the job after the fact, and in the environment when the job runs.
It does work if you call it using a build.properties file from an upstream job.

An example usage of the URL call is this:
wget -O - "http://hudsonmaster1.uk.nds.com:8080/hudson/job/TEST_EXTENDED/buildWithParameters?token=hudson-ci&FIRST=MyTest&SECOND=XXX"

TEST_EXTENDED is my test job with FIRST as a normal String parameter, SECOND is an extended choice parameter where XXX is a valid option.

All the job does is this, as a build step:
echo $FIRST
echo $SECOND