When --JENKINS-27295-- was implemented there was a specific serialisation check in place that blocked RunParamaterValue from adding to the params array that provides access to the real object, rather than a string representation of it.

On some recent testing if an input step is used to request a build be selected:

  wah = input message: '', parameters: [run(description: '', filter: 'SUCCESSFUL', name: '', projectName: 'cme/example_02_artefact/master')]

Then the object returned is the Run object that you can then do getDisplayName or getDescription on ...

If instead of an input step a build parameter is used: 

properties([parameters([run(description: 'Select the version of the artifact to deploy', filter: 'SUCCESSFUL', name: 'deploy_artifact', projectName: 'cme/example_02_artefact/master')])])

Then the variable (direct or through env.foo) is just the $BUILD_URL of the build selected as a string, and there's no Run object on params to access more detail about that build.

These should be made consistent so that either the input step only returns the string job_url to match the build params, or the Run object itself should be accessible when using a build parameter ... naturally I'd prefer the latter as it's way more flexible.