I wasn't just blindly assuming the alias worked the same. I actually read the Compare-Object documentation [1], which contains that exact command as an example of how to compare files. I just didn't understand the sort of comparison it did.
If you search "PowerShell compare two files", it becomes pretty clear this is a common confusion even among people using the name Compare-Object. For example, the top serverfault question has an incorrect top-voted, accepted answer [2].
Well, perhaps some hypothetical "you" uses them:) To be clear, I run 100% genuine Bourne-family shells on unix-like systems, and merely visit MS-land for sightseeing;)
Compatibility layers are great, when they're actually compatible. Almost-compatible layers are a nightmare.