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You can compare their ids to see if they are the same.

{if $addresses.invoice.id eq $addresses.delivery.id}

like this

{if $addresses.invoice.id eq $addresses.delivery.id}
  <tr>
      <td width="100%" colspan="2"><span class="bold">{l s='Billing Address' d='Shop.Pdf' pdf='true'}</span><br/>
          {$invoice_address}
      </td>
  </tr>
{else}
  <tr>
      <td width="50%">
          {if $delivery_address}<span class="bold">{l s='Delivery Address' d='Shop.Pdf' pdf='true'}</span><br/>
              {$delivery_address}
          {/if}
      </td>
      <td width="50%"><span class="bold">{l s='Billing Address' d='Shop.Pdf' pdf='true'}</span><br/>
          {$invoice_address}
      </td>
  </tr>
{/if}