Use the second one:
$this->set('countries', $this->Institute->Country->find('list', $params = array('fields' => array('id', 'country'))));
Both work, but, you've already got an instance of your country model (accessible via $this->Institute->Country). So, why create another instance of it? There's just no need.
There shouldn't actually be a need to specify the fields for your call to the find method. 'id' will be automatically selected as the first field, and if you set the display field of your Country model to 'country', then that will be the default uses in find('list') calls. Do it like this:
// just after class Country extends AppModel {
public $displayField = 'country';
Then, you'll just need to use this code:
$this->set('countries', $this->Institute->Country->find('list'));