HTTP 1.1 is a protocol that has nothing to do with the Operating System. It's used by browsers. Its main advantage over HTTP 1.0 is that it will use the same TCP connection for several HTTP requests by default (this is called Persistence in 1.1), whereas with HTTP 1.0 by default you establish one TCP connection for each HTTP Transaction - which is a waste of network performance and usage.
So your question is really: Is the HTTP 1.1 implementation different in IE8 depending on the OS? It's entirely possible. You could check the Apache access.log, but it's a pain in a neck to look into that. You're better off installing Wireshark and capturing your HTTP requests from each of the computers. To compare the requests, simply identify the correct TCP connection, right click, and do a "Follow TCP Stream". It will then show you a re-assembled text version of all the packets and you will see the HTTP Headers and Body from both the client and server side.