Try this for people that keep toggling between 4G and 3G:
I think I have figured out how to get LTE+CDMA only on the S3, so that when you have a 1-2 bar 4G signal the phone doesn't automatically go into a full bar 3G mode as a preference. I know this may kill the battery somewhat faster, but I for one would prefer a 1-2 bar 4G signal that is faster than a full bar 3G signal. I went into ##3282## >> Edit >> Put in MSL >> eHRPD >> eHRPD off. You should now not be able to connect to a 3G signal at all. This is just a hunch though. I get good 4G at my house, so until I go out again, I won't be able to thoroughly test my theory.
I think the phone is too quickly changing a 1-2 bar 4G signal back to full bar 3G probably to conserve battery. I think this might be a work around for it. Test it out and let me know if that fixes it.