It could improve performance but it may not
If your OS is 64-bit and you run a 32-bit application, all the API calls have to be thunked to their 64-bit equivalents. The WOW64 subsystem in Windows is quite robust but even so I imagine that in a graphics & text intensive application like Firefox that this could have an effect. Also, if Firefox were the only 32 bit app you were using on the system, then you incur a memory overhead of loading up the thunk DLLs.
On the other hand, the instructions and memory requirements for 64-bit apps are higher. This may mean that some internal assumptions that Firefox may make such as the amount of memory to reserve for cache, the amount of memory to reserve in certain objects like auto strings may be incorrect for the architecture. Other things like the JS to C++ marshalling assembly code might be non-optimal. These sorts of things could require a lot of tuning before comparing versions. Even for comparison purposes you might need to allow more memory to fairly compare a 64-bit apps to its 32-bit version.
Additionally Firefox has to decide what to do with 32-bit plugins and 32-bit add-ons. Does it support them or not. If not, then that limits the reasons for using 64-bit and also drags up the issue of WOW64 again.
So while I wouldn't say a 64-bit firefox would scream ahead of the 32-bit counterpart, it may provide a modest boost if you have enough memory to run it and once the kinks have been ironed out.