He says "1Mbit more" so it's 4+1 to 5+1 = 5-6 Mbit/s =)
have a cup of coffee, that should get rid of your deep-sleep problem.
The most annoying thing sometimes you have full signal, open a website and there is like a 15 second hang. Tried different modems, fast dormancy settings and nothing seems to work.
Please verify if both mobile phones are connected to the same antenna.
The S3 is blazing fast (compared to iPhones), however I've had the same issue as you.
The reason was that my provider kept (and still keeps trying) to push APN settings with a stupid HTTP-proxy which is completely overloaded and half of the time breaks the connection anyway.
Just remove the proxy IP (if any) from the APN settings, verify it's gone and try again.
If you have an account to paid VPN, you can also try this as it should give the same accelerated speed.