Different Front page for Mobile

Switching the actual template file could work in the same way as above using get_template_part().

For example…

<?php
if ( wp_is_mobile() ) { // If it is a mobile device

get_template_part( 'mobile-front', 'page' );

} else { // If it is not a mobile device

get_template_part( 'desktop-front', 'page' );

} // end wp_is_mobile()

To take this a step further…

You could add a filter on template_include to load the specific template file using wp_is_mobile() to determine which template file to load.

The Codex info for template_include.