Reading official docs it\'s obvious that PowerShell -match operator is more powerful than -like (due to regular expressions). Secondly, it seems ~1
You should prefer -like when your comparator string is a dos-style filename wildcard. If you have a cmdlet that is designed to look like a "standard" windows command line application, then you can expect file name parameters to include dos-style wildcards.
You might have a grep-like cmdlet that takes a regex and a list of files. I can imagine it being used like this:
> yourMagicGrepper "^Pa(tt).*rn" *.txt file.*
You would use -match when working with the first parameter, and -like for all other parameters.
In other words: it depends on your functional requirements.