128 bit, 64 bit, 32 bit, blaargh...
I'm afraid you've all been "bitten"

by the marketing folks.
If you think Megahertz is an inaccurate way to measure performance, don't even get started talking about "bit"ness.
Data width has been used by the marketing folks (primarily at the game console companies) as a way of claiming superiority. In reality, it's usually a load of crap. Many of these comparisons aren't even comparing the components of the machines they're attempting to compare.
However, if it matters, *usually* when a chip manufacturer says that a processor is 32-bit or 64-bit, they're referring to how much memory can be addressed by the processor (which is generally determined by the width of the registers). And the most significant thing that matters in this case is how much memory can be addressed by the processor (about 4GB with 32 bit addressing). It could also be used to perform floating point computations with higher accuracy (something that generally has no impact on performance).
However, sometimes "bit"-ness refers to the data path to memory, which is one of the primary factors in how fast you can move information from RAM to the processor (currently 64-bit in the PowerMacs). The other primary factor is the bus speed (133Mhz in the PowerMac).
The Altivec is a little bit interesting in the way it works. The Altivec unit does indeed use 128 bit registers. Wider is better because you can fit several smaller groups of information into the same register and then perform a computation on all the information at the same time. However, this is very unique to Altivec. It is not something that happens in general use. If you're using a 64-bit processor (the G4 is a 32-bit processor in the memory-addressing nomenclature), you're really only going to see an advantage if you need to address a *lot* of memory, or you have some other really unique situations.
If it's Sony marketing the Playstation, they're just finding the widest datapath in the machine and quote that number because it's the biggest. IE, if they have special graphics hardware with a 128-bit path to memory, suddenly the Playstation is a "128 bit" machine (regardless of the 20-year-old embedded processor variants used to run the machine.)