try {
    $response = Invoke-WebRequest @myparams -EA Stop
    # do more stuff with the response
} catch [System.Net.WebException] {
    # parse the JSON response body for error details
}

try {
    $response = Invoke-WebRequest @myparams -EA Stop
    # do more stuff with the response
} catch [System.Net.WebException] {
    # Desktop: parse the JSON response body for error details
} catch [Microsoft.PowerShell.Commands.HttpResponseException] {
    # Core: parse the JSON response body for error details
}