Powershell sort command not working as expected

PowerShell - unlike direct use of .NET types - is case-insensitive by default; you need to opt in if you want case-sensitive behavior.

In the case of Sort-Object you need to use its -CaseSensitive switch:

PS> -join ('a', 'B', 'A', 'b' | Sort-Object -CaseSensitive)
aAbB

As you expected, this results in lowercase letters sorting first, because in the (US-English) collation order lowercase letters have lower sorting weight than uppercase ones - even though with respect to their Unicode code points the relationship is reversed (e.g., [int] [char] 'a' is 97, whereas [int] [char] 'A' is 65).

(Code-point-based sorting would apply if the array contained [char] instances, but PowerShell has no [char] literals, so a literal such as 'a' is a [string] of length 1; you can use explicit casts, however: -join ([char] 'A', [char] 'a' | Sort-Object -CaseSensitive) yields 'Aa', i.e. sorts uppercase first.)

Without -CaseSensitive, the lowercase and uppercase variants of a given letter have equal sorting weight, so no particular ordering among them is guaranteed.

For instance, the following loop exits quickly:

$prevResult = $null
while ($true) { 
  
  # Get a shuffled array of lower- and uppercase letters.
  $arr = 'a', 'B', 'A', 'b'
  $arr = $arr | Get-Random -Count $arr.Count
  
  # Sort it case-INsensitively.
  $result = -join ($arr | Sort-Object)

  $result # output

  # See if the result is different from the previous one.
  # Note the use of -cne rather than just -ne:
  # -ce is the case-*sensitive* variant of -ne
  if ($prevResult -and $prevResult -cne $result) {
    Write-Warning "Output order has changed."
    break
  }
  $prevResult = $result

} 

However, for a given input array, the two PowerShell editions differ with respect to sort stability, i.e. whether the input order of elements that sort the same is preserved:

• In Windows PowerShell, Sort-Object is invariably not stable.

• In PowerShell (Core) 7, Sort-Object now has a -Stable switch to request stable sorting, but - as of v7.4.x - it appears that sorting is stable by default (and, conversely, -Stable:$false does not opt-out). That said, to be future-proof and for conceptual clarity, it is better to specify -Stable explicitly when needed.

Here's a quick example that illustrates the difference:

# PowerShell 7 (as of v7.4.x works the same even without -Stable)
# -> 'AabBCc', i.e. input order was preserved.
-join ('A', 'b', 'C', 'a', 'B', 'c' | Sort-Object -Stable)

# Windows PowerShell (no -Stable switch)
# -> !! 'aABbcC', i.e. the input order was *not* preserved.
-join ('A', 'b', 'C', 'a', 'B', 'c' | Sort-Object)