Difference between bloginfo(‘home’) and home_url() and site_url()

The difference in your case is in filters being applied to output of these functions.

While bloginfo applies one of these filters:

if ( 'display' == $filter ) {
        if ( $url )
            $output = apply_filters('bloginfo_url', $output, $show);
        else
            $output = apply_filters('bloginfo', $output, $show);
    }

Function home_url applies this filter:

return apply_filters( 'home_url', $url, $path, $orig_scheme, $blog_id );

Adn finally site_url applies this filter:

return apply_filters( 'site_url', $url, $path, $scheme, $blog_id );

It is true that bloginfo uses one of mentioned functions (home_url and site_url). It is clear from its source code:

function get_bloginfo( $show = '', $filter="raw" ) {

    switch( $show ) {
        case 'home' : // DEPRECATED
        case 'siteurl' : // DEPRECATED
            _deprecated_argument( __FUNCTION__, '2.2', sprintf( __('The <code>%s</code> option is deprecated for the family of <code>bloginfo()</code> functions.' ), $show ) . ' ' . sprintf( __( 'Use the <code>%s</code> option instead.' ), 'url'  ) );
        case 'url' :
            $output = home_url();
            break;
        case 'wpurl' :
            $output = site_url();
            break;
...

From this piece of code, it is clear that when calling bloginfo(‘home_url’) or bloginfo(‘site_url’), all mentioned filters ale applied. When calling home_url or site_url, bloginfo’s filters are not applied.

The thing is, that qTranslate, probably, hooks only bloginfo’s filters.