"Error: Undefined class constant 'Symfony\Component\DependencyInjection\ContainerInterface::SCOPE_CONTAINER'"
The problem is exactly that you executed composer update twice, in two different directories. You don't execute it from the core directory, but only from the directory containing the core directory. In fact, the composer.json file you find in the directory where you decompressed the Drupal archive contains the following lines.

    "merge-plugin": {
        "include": [
            "core/composer.json",
        ],
        "recurse": false,
        "replace": false,
        "merge-extra": false
    }


The include part is telling to Composer to include the core/composer.json file too when updating. Supposing that mysite is the directory containing the core directory and the other Drupal files, it is enough you execute the following commands to get in mysite/vendor all the dependencies necessary.

cd mysite
composer update


In my case, I get the following output. (It may change, basing on how often you execute those commands.)


  Loading composer repositories with package information
  Updating dependencies (including require-dev)
     Removing symfony/polyfill-iconv (v1.1.1)
     Installing symfony/polyfill-iconv (v1.2.0)
       Downloading: 100%         
  
  Drupal\Core\Composer\Composer::vendorTestCodeCleanup
    Removing symfony/polyfill-mbstring (v1.1.1)
    Installing symfony/polyfill-mbstring (v1.2.0)
      Downloading: 100%         
  
  Drupal\Core\Composer\Composer::vendorTestCodeCleanup
    Removing symfony/polyfill-php54 (v1.1.1)
    Installing symfony/polyfill-php54 (v1.2.0)
      Downloading: 100%         
  
  Drupal\Core\Composer\Composer::vendorTestCodeCleanup
    Removing symfony/polyfill-php55 (v1.1.1)
    Installing symfony/polyfill-php55 (v1.2.0)
      Downloading: 100%         
  
  Drupal\Core\Composer\Composer::vendorTestCodeCleanup
    Removing guzzlehttp/promises (1.1.0)
    Installing guzzlehttp/promises (1.2.0)
      Downloading: 100%         
  
  Drupal\Core\Composer\Composer::vendorTestCodeCleanup
    Removing symfony/polyfill-apcu (v1.1.1)
    Installing symfony/polyfill-apcu (v1.2.0)
      Downloading: 100%         
  
  Drupal\Core\Composer\Composer::vendorTestCodeCleanup
  Writing lock file
  Generating autoload files
   Drupal\Core\Composer\Composer::preAutoloadDump
   Drupal\Core\Composer\Composer::ensureHtaccess


Both Drupal 8 and Drush work for me.

drush status



  Drupal version                  :  8.1.1
  Site URI                        :  http://default
  Database driver                 :  mysql
  Database hostname               :  localhost
  Database port                   :
  Database username               :  database_username
  Database name                   :  database_name
  Drupal bootstrap                :  Successful
  Drupal user                     :
  Default theme                   :  bartik
  Administration theme            :  seven
  PHP configuration               :  /etc/php.ini
  PHP OS                          :  Darwin
  Drush script                    :  /usr/local/bin/drush
  Drush version                   :  8.0.5
  Drush temp directory            :  /tmp
  Drush configuration             :
  Drush alias files               :
  Install profile                 :  standard
  Drupal root                     :  /Library/Server/Web/Data/Sites/mysite
  Drupal Settings File            :  sites/default/settings.php
  Site path                       :  sites/default
  File directory path             :  sites/default/files
  Temporary file directory path   :  /tmp
  Sync config path                : sites/default/files/config_WZrobbGFfHIWBRmKDknFVfKgdyG1gKNFLBYcpBlbTZtEarG_rPEixLJFW6faE9yNFTjdkieQbA/sync


As side note, if you need to include the composer.json files modules could have, you can edit the mysite/composer.json file to contain the following lines.

    "merge-plugin": {
        "include": [
            "core/composer.json",
            "modules/*/composer.json"
        ],
        "recurse": false,
        "replace": false,
        "merge-extra": false
    }


Alternatively, you can use the Composer Manager module. I would suggest installing it, if you need to include any dependecy modules could have.