Web testing Difference of SOAP 1.1 and 1.2

I'd go a bit further and recommend using our web service testing tools SoapUI (free) or ReadyAPI. They are specifically tailored for SOAP and REST service testing, support all major SOAP standards (SOAP 1.1/1.2, MTOM, WS-Addressing, WS-Security, etc.), provide easy request parameterization (using project variables and data from previous requests), include lots of SOAP and XML assertions (XPath Match, Not SOAP Fault, Valid HTTP Status Codes, etc.). SoapUI/ReadyAPI tests can also be integrated into TestComplete projects.

To answer your original question, you should use MSXML 6.0 - it's the most recent version and is included in all Windows versions since Windows XP SP3. MSXML 3.0 may be used as a fallback, but 6.0 should work in most (all?) scenarios.
https://en.wikipedia.org/wiki/MSXML#Versions

http://blogs.msdn.com/xmlteam/archive/2006/10/23/using-the-right-version-of-msxml-in-internet-explorer.aspx

Alternatively, you can use TestComplete's WebServices project item (as AlexKaras suggested), or the aqHttp object included in TestComplete 12.40+, which provides similar functionality to MSXML2.XMLHTTP.

SOAP 1.1 and 1.2 use a slightly different request format, so make sure you use the correct request headers and body.

For example, using this calculator service:
http://www.dneonline.com/calculator.asmx

SOAP 1.1 request:

POST /calculator.asmx HTTP/1.1
Host: www.dneonline.com
Content-Type: text/xml; charset=utf-8
Content-Length: <length>
SOAPAction: "http://tempuri.org/Add"

<?xml version="1.0" encoding="utf-8"?>
<soap:Envelope
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema"
    xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/">
  <soap:Body>
    <Add xmlns="http://tempuri.org/">
      <intA>2</intA>
      <intB>3</intB>
    </Add>
  </soap:Body>
</soap:Envelope>

SOAP 1.2 request:

POST /calculator.asmx HTTP/1.1
Host: www.dneonline.com
Content-Type: application/soap+xml; charset=utf-8
Content-Length: <length>

<?xml version="1.0" encoding="utf-8"?>
<soap12:Envelope
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema"
    xmlns:soap12="http://www.w3.org/2003/05/soap-envelope">
  <soap12:Body>
    <Add xmlns="http://tempuri.org/">
      <intA>2</intA>
      <intB>3</intB>
    </Add>
  </soap12:Body>
</soap12:Envelope>