Start-job vs. Invoke-command -asjob
The first example using start-job does not use HTTP for the call and instead uses an IPC channel with WinRM to run; it does not require administrative privileges this way. The second example with invoke-command does require admin rights (by default) and will connect via HTTP and WinRM.
To be honest, I would have expected the second one to fail for most people. If you run: Receive-Job against the ID of the start-job invocation, do you get any error messages?
-Oisin
To receive an updated JobStateInfo you'll need to use Get-Job and the job created by Start-Job. Though, if you're using this information to see when the job finishes, Wait-Job or Receive-Job -wait might be better suited to your needs.
Wait-Job simply waits until the job, or list of jobs, indicated is finished before moving on. Receive-Job -wait does the same thing, but it also gathers the results/output of the job.