Possible Fix, Please test.
My family has 3 different iphone 5's and they are all doing the same thing. All other iphones and ipads in the house get the expected results on speedtest.net app. But our iPhone 5's get around half of what the other iOS 6 devices are getting over Wifi on the same servers.
I have fixed the issue on our phones by going into Settings/Wifi/Blue arrow next to your Wifi name/ and typing test into Client ID and then renew lease.
No idea why it helps but I was trying everything to get it working because I was blowing through my LTE not wanting to deal with slow Wifi. Issue completely resolved after doing this. Makes me think it is just a software bug that is only affecting iPhone 5's on ios 6 and will likely be fixed when ios 6.0.1 is released.
Please let me know if this helps in your situations... Could be exclusive to my Wi-Fi setup (I run all Airport Extremes and Airport Expresses).