I thought I knew the answer to this question, but decided to do some checking before answering.
It turns out that current Core Duo and Core Solo processors are 32-bit. I couldn't find confirmation of this on either Apple or Intel's web sites, but found confirmation of this fact in the following Wikipedia article:
http://en.wikipedia.org/wiki/Intel_Core.
32-bit vs 64-bit isn't really about speed directly. As I understand it, and I don't profess to have real knowlede in this area, the main benefit of 64-bit is that it can directly address more memory. When a processor can directly access more physical RAM, this in turn makes it faster when dealing with large data sets.
Intel also have a technology for some of their 32-bit processors called
EM64T, which allows them to do 64-bit memory addressing. That is (from my understanding), they are still 32-bit processors, but support 64-bit general purpose registers, 64-bit integer arithmetic and logical operations, and 64-bit virtual addresses. However, the current Core Duo and Core Solo processors do not support EM64T according to the Wikipedia article, but the next version (code named Merom) will.
What I found particularly interesting though is that the
Core platform is a platform of mobile processors. That is, the processors are intended for notebooks, despite the fact Apple is using them in the new iMac. This suggests that the Core Duo processor won't make it into whatever replaces the PowerMac. Instead it is more likely that a new desktop processor, using similar technologies, will be used.