12.10 64bit should be your choice.
hard to say which one is better. depends what you are trying to acomplish. and what you would like to have.
+ newer kernel (means better support for new hardware, also newer drivers included). your CPU and GPU chip is quite new on the market i believe.
+ newer programmes
+ new features
+ improved interface
- stability maybe (for some it is working very well) not as good as in 12.04
- no unity 2D, fallback mode not as good.
+ five year support (until 2017) with security updates and big fixes
+ better stability of the OS
+ various good fallback modes (gnome fallback, unity 2D)
- older kernel (=older drivers)
- older versions of programmes
a big difference. There are no apps that will only install on a 32-bit system that I'm aware of, and I've been running 64-bit for years. There used to be a few (eg: Flash), but those days are long-gone. It really is trouble-free these days, I recommend anyone who can runs 64-bit. The amount of RAM you have is immaterial. I have 4GB of RAM, and have been running 64-bit ever since my system only had 2GB.
Embrace the 64-bit, it's lovely
by having 4GB RAM I meant that 32 bit can use upto 4GB RAM to use RAM more than 4GB 64 bit is necessary.
regarding apps support 32bit only I was about to say android sdk but I checked and now they are also in 64 bit , but to install latest ATI driver we must have 32 bit libraries
Anyway 64 bit is obviously better than 32 bit in many aspects so no point of discussion here. He can use 32 or 64 as per his choice