Its not true that more RAM is required for 64 bit. The thing is it can support upto 128 GB of RAM whereas 32bit can only support upto 4 GB of RAM.
There is a bit od performance difference on 64 bit compared to 32 bit, but you wont feel it until you measure the timings in miliseconds as done by testers or you use a extensive application like Photoshop or any video editor.