Could drush require significantly more memory than same action in Drupal
Probably not - but remember that in PHP 5, the command line or client interface for PHP was separated out and has its own ini file. if you search for your php.ini file, you'll probably see two versions, something like this

/etc/php5/cli/php.ini
/etc/php5/apache/php.ini


and you just need to match the memory limit in the (cli)ent ini file with what you have for Apache (or your web server).