When both ticket providers, Tickets Commerce, and WooCommerce, are active at the same time, the default ticket provider is Tickets Commerce.
If you prefer to set WooCommerce as the default ticket provider, you can do so with the following snippet.
add_filter( 'tribe_tickets_get_default_module', 'et_default_ecommerce_module', 10, 2 );
function et_default_ecommerce_module( $default, $modules ) {
// TC - TEC\Tickets\Commerce\Module
// Woo - Tribe__Tickets_Plus__Commerce__WooCommerce__Main
$my_default = 'Tribe__Tickets_Plus__Commerce__WooCommerce__Main';
return in_array( $my_default, $modules ) ? $my_default : $default;
}