If else statement based on date_diff value

You can use strtotime() to convert the time to an integer, and then do a conditional.

// Get the current time
$now = strtotime("now");
// Convert post's modification time to int
$postUpdated = strtotime( $post->post_modified );
// Check if 3 hours has passed, each hour is 60*60 seconds
if ( $now - $postUpdated >= 3*60*60 ) {
    // First conditional
} else {
    // Second conditional
}

Also, if the time’s format is known ( which is usually 0000-00-00 00:00:00 ), you can directly use strftime(). Here is a quick example:

$timestamp = strftime("%Y-%m-%d %h:%M:%S %a", time() - 3*60*60);

Now you have a formatted value of 3 hours before, which you can use in date_diff().