More elegant way to compare multiple array values in PowerShell

You can do array intersection quite easily with this:

$keyModes = 'Role', 'RoleService', 'Feature'
if ($keyModes | ? { $ProcessingModes -contains $_ }) { "found at least one" }

Your question is basically, is there an operator in PowerShell which determines whether the intersection between two arrays is non-empty. The answer is no, there is not. Additionally, after reviewing the question Powershell, kind of set intersection built-in?, it looks like the best approach is to use HashSet objects instead of arrays, which do expose IntersectWith and UnionWith methods.

You could use a RegEx instead. Here's how I would do it:

$ProcessingModes = @('Role','Service')
if ($ProcessingModes -match '\b(Role|RoleService|Feature)\b') {
    'it matches'
} else {
    'it does not match'
}
it matches

$ProcessingModes = @('RoleGroup','Service')
if ($ProcessingModes -match '\b(Role|RoleService|Feature)\b') {
    'it matches'
} else {
    'it does not match'
}
it does not match

The \b is a word boundary. It's equivalent to search "as whole word". It's not absolutely necessary in your code because of your ValidateSet, but it would provide useful to avoid finding "Role" in another word like "RoleGroup" if you ever permit it. You could try removing both \b in the second example to see it matches.

I think this will make your code more readable and probably more elegant.

Since at least Powershell 5.1 you can use Compare-Object for comparing two arrays of values. A simplified example

$ProcessingModes = 'Service', 'Role', 'RoleService', 'Feature', 'Group', 'File', 'Package'
$ModesToCompare = 'Role', 'RoleService', 'Feature'

$Comparison = Compare-Object -ReferenceObject $ProcessingModes -DifferenceObject $ModesToCompare -IncludeEquals

$Comparison will give you the following output:

InputObject SideIndicator
----------- -------------
Role        ==
RoleService ==
Feature     ==
Service     <=
Group       <=
File        <=
Package     <=

This means that Service, Group, File, and Package only existed in the -ReferenceObject. By adding the -IncludeEquals you get exactly what you're looking for. You can now take this output and check if SideIndicator contains ==, like so:

if($Comparison.SideIndicator -contains "=="}
    #some code here
}