Visualforce - COUNT() vs COUNT_DISTINCT()

Having COUNT_DISTINCT() is a great advantage in apex over standard Salesforce reporting capabilities. Still what you need to remember is that it doesn't return Integer (as COUNT() is doing), but List<AggregateResult> with count stored in the expr0 attribute of the first element of the list.

So while the following code is valid:

public String getObjectsForSelectedApplication() {
        return String.valueOf([SELECT COUNT() 
FROM MyObjects__c WHERE Application__c = :selectedApplication]);
}

The following code will return a list:

public String get UniqueUsersForSelectedApplication() {
        return String.valueOf([SELECT COUNT_DISTINCT(User__c) 
FROM MyObjects__c WHERE Application__c = :selectedApplication]);
}

What you need to do is take the count from the list, for example with the following code:

  public String getUniqueUsersForSelectedApplication() {
        List<AggregateResult> result = [SELECT COUNT_DISTINCT(User__c) 
FROM  MyObjects__c WHERE Application__c = :selectedApplication];
        if (result.isEmpty()) {
            return '0';
        } else {
            return String.valueOf(result.get(0).get('expr0'));
        }
    }