Compare-Object is convenient, but indeed slow; also avoiding the pipeline altogether is important for maximizing performance.
I suggest using a [System.Collections.Generic.HashSet[T] instance, which supports high-performance lookups in a set of unordered[1] values:[2]
# Two sample arrays
$localmd5 = 'Foo1', 'Bar1', 'Baz1'
$remotefilehash = 'foo1', 'bar1', 'bar2', 'baz1', 'more'
# Create a hash set from the local hashes.
# Make lookups case-*insensitive*.
# Note: Strongly typing the input array ([string[]]) is a must.
$localHashSet = [System.Collections.Generic.HashSet[string]]::new(
[string[]] $localmd5,
[System.StringComparer]::OrdinalIgnoreCase
)
# Loop over all remote hashes to find those not among the local hashes.
$remotefilehash.Where({ -not $localHashSet.Contains($_) })
The above yields collection 'bar2', 'more'.
Note that if case-sensitive lookups are sufficient, which is the default (for string elements), a simple cast is sufficient to construct the hash set:
$localHashSet = [System.Collections.Generic.HashSet[string]] $localmd5
Note: Your later feedback states that $remotefilehash is a hashtable(-like) collection of key-value pairs rather than a collection of mere file-hash strings, in which the keys store the hash strings. In that case:
To find just the differing hash strings (note the .Keys property access to get the array of key values):
$remotefilehash.Keys.Where({ -not $localHashSet.Contains($_) })
To find those key-value pairs whose keys are not in the hash set (note the .GetEnumerator() call to enumerate all entries (key-value pairs)):
$remotefilehash.GetEnumerator().Where({ -not $localHashSet.Contains($_.Key) })
Alternatively, if the input collections are (a) of the same size and (b) have corresponding elements (that is, element 1 from one collection should be compared to element 1 from the other, and so on), using Compare-Object with -SyncWindow 0, as shown in js2010's helpful answer, with subsequent .SideIndicator filtering may be an option; to speed up the operation, the -PassThru switch should be used, which forgoes wrapping the differing objects in [pscustomobject] instances (the .SideIndicator property is then added as a NoteProperty member directly to the differing objects).
[1] There is a related type for maintaining sorted values, System.Collections.Generic.SortedSet[T], but - as of .NET 6 - no built-in type for maintaining values in input order, though you can create your own type by deriving from [System.Collections.ObjectModel.KeyedCollection[TKey, TItem]]
[2] Note that a hash set - unlike a hash table - has no values associated with its entries. A hash set is "all keys", if you will - all it supports is testing for the presence of a key == value.