You have to override
module_checkout/view/frontend/web/template/shipping-address/list.html
or
module_checkout/view/frontend/web/template/shipping-address/address-renderer/default.html
list.html
<!-- ko if: (visible)-->
<div class="field addresses">
<div class="control">
<select>
<!-- ko foreach: { data: elems, as: 'element' } -->
<!-- ko template: element.getTemplate() --><!-- /ko -->
<!-- /ko -->
</select>
</div>
</div>
<!-- /ko -->
or default.html
<option>
<!-- ko text: address().firstname --><!-- /ko --> <!-- ko text: address().lastname --><!-- /ko --><br/>
<!-- ko text: address().street --><!-- /ko --><br/>
<!-- ko text: address().city --><!-- /ko -->, <!-- ko text: address().region --><!-- /ko --> <!-- ko text: address().postcode --><!-- /ko --><br/>
<!-- ko text: getCountryName(address().countryId) --><!-- /ko --><br/>
<!-- ko text: address().telephone --><!-- /ko --><br/>
</option>
this will display you an shipping address in dropdown, but i don't about how to set selection event for shipping address as of billing address, for that may be you have to look at module-checkout/view/frontend/web/template/billing-address/list.html
or module-checkout/view/frontend/web/js/view/billing-address.js