My First Suggestion would be to run wireshark on the 32bit Machine, and then browse the net on the 64Bit machine. Can you see the traffic? Probally not.
What i have noticed and i could be way off basics but the fact is that the traffic from the other machine is not blasted through the hole network and your not gonna be able to see it. If the machine your trying to see traffic from is on the wired side and your on wireless, or your both wired into the AP, then your just not going to see the traffic.
I would suggest first either MITM the 64 bit machine then fire up hamster and ferret you will have better luck.