Should I downgrade the Galaxy Nexus?

I live in an area which doesn't necessarily get the latest updates, so when Android 4.2 was released, I flashed it on my Galaxy Nexus (which was running 4.0.4 at the time). The problem is that it gets insanely hot while doing menial tasks and battery it pathetic.

So, should I flash 4.1.2 on it? I don't know how the Galaxy Nexus performed on it since I never used it. Also, I don't want for 4.3, since by that time it will have passed on to my sister (who really couldn't care less as to what software version it is running). Any Galaxy Nexus owners, let me know if 4.1.2 was better than 4.2.2.

P.S. I know that this is kind of late, but I just couldn't bear these issues anymore.