Thanks, this works from both clients: $x.guest.ExtensionData.GuestFamily
And that's all I really need. But in case I'm not the only one interested in solving the mystery, here are results of get-powerCLIversion...
...from my desktop:
PowerCLI Version
----------------
VMware vSphere PowerCLI 5.1 Release 1 build 793510
---------------
Snapin Versions
---------------
VMWare AutoDeploy PowerCLI Component 5.1 build 768137
VMWare ImageBuilder PowerCLI Component 5.1 build 768137
VMware vCloud Director PowerCLI Component 1.5 build 793505
VMware License PowerCLI Component 5.1 build 669840
VMware vSphere PowerCLI Component 5.1 build 793489
...and from client2:
PowerCLI Version
----------------
VMware vSphere PowerCLI 5.1 Release 1 build 793510
---------------
Snapin Versions
---------------
VMWare AutoDeploy PowerCLI Component 5.1 build 768137
VMWare ImageBuilder PowerCLI Component 5.1 build 768137
VMware vCloud Director PowerCLI Component 1.5 build 793505
VMware License PowerCLI Component 5.1 build 669840
VMware vSphere PowerCLI Component 5.1 build 793489
In case it's relevant, this was the only version of PowerCLI ever installed on client2. With PowerCLI already installed there, I did upgrade Powershell from v2 to v3.