The main advantage of a higher bit system over a lower one is being able to move around larger chunks of data at a given time, namely 64 bits rather than 32 bits. This does spped up operations that use large amounts of data, such as photoshop, since it can now move twice as much data with a single operation. The advantage of being able to address more memory is, in my opinion ALMOST just a side effect. It does, of course, help in the same way that adding more memory helps on any system, but it is not a fundemental change.
The advantages of moving to a higher bit system are especially hilighted if you try to program on an eight bit system. For example, try writing a program to add two sixteen bit number, such as 10 and 11, hex (16 and 17 decimal). On an eight bit system, this is somewhat complex. You have to input the two low order bytes (0 and 1) add them, store them somewhere, input the two high order bytes, add them with the cary from the low order bytes, then store them somewhere. That is five operations just to add two numbers. On a sixteen bit system, it would be three operations: load, add, store. All other things being equal, you have just gotten a processor that is 40% faster, at least on an add operation with numbers larger than 8 bits. On the other hand, for numbers smaller than 8 bits, there is no speed increase. Same number of operations on the same processor speed = same execution time, regardless of the bit size the processor can handle. When going from 8 bits to 16 or 32, pretty much everything benifits, because most chunks of data handled will be larger than 8 bits. going from 32 to 64 at the current time will not have nearly as much noticable impact as going from 8 to 16 or 16 to 32, becasue most calculations currently done deal with numbers smaller than 32 bits, however certain applications such as graphics and video applications that have to calculate HUGE numbers will benifit. It is also possible that other applications such as iTunes could be rewriten to take advantage of this, perhaps somehow combining two seperate operations into one, but that would take more work.