The benefit of WireShark is that it could possibly show you errors in levels below the HTTP protocol. Fiddler will show you errors in the HTTP protocol.
If you think the problem is somewhere in the HTTP request issued by the browser, or you are just looking for more information in regards to what the server is responding with, or how long it is taking to respond, Fiddler should do.
If you suspect something may be wrong in the TCP/IP protocol used by your browser and the server (or in other layers below that), go with WireShark.