For me anyway, I'm leaning toward some sort of a compatibility issue with the Speed Test app and the iPhone 5 (not necessarily iOS 6).
This morning I cleared the cookies and caches on both my iPhone 4S and iPhone 5, (and re-started them as well) then compared real-world browsing speeds. (both run iOS 6) The iPhone 5 was always faster. Yet if i ran the Speed Test application, the iPhone 5 faired poorly with speeds being about a third as fast as the iPhone 4S.
No matter how many times I ran the the test, it was always the same; real world browsing, the iPhone 5 is fastest, the Speed Test app shows something entirely different.
As far as connection issues, I was unable to connect to parent's wifi yesterday, getting the "password is incorrect" error message. I'm sure the password that I entered is fine however. Could be pilot error, I'll look into it.
I'll see if I can connect to our public wifi at work today... it is wide open.
Update: Connected at work without a hitch.