It does mean an upgrade for what the user is capable of doing.
A 32 bit system/program runs out of memory at around 3.8 GB of memory usage, because it runs out of bits to actually put into said memory.
Your game would have for sure crashed once it hit the magic 3.8 gig mark.
More RAM is used, so the game has more space to add stuff on to, like in the most simple case, world generation, larger world's require more space to assign everything, and that's not even counting the history that's applied on top of it.
It also in theory should help with FPS death in larger forts.
What 64 bit won't/shouldn't do would be to actually run the 4 GB of memory through at any reasonable speed (ex. A 16x16 embark), since any changes must be handled by the processor, then fed back into RAM, so it can do another calculation after that. The key difference is that it CAN run now, with more than 4 GB of RAM. For higher performance, you need a faster unit (higher clockrate, usually), a bigger buffer (effectively more RAM/working space inside the processor), or multithreading.
If you want better program specific performance, you are going to have to multithread, which is a whole other can of worms from a programming perspective, which essentially means core 1 of your processor, for example would handle movement, while core 2 handled projectiles in flight, and core 3 does something else, like simulating the damage caused by that projectile impact.
If multuthreading was a thing already in place, it's probable that water movement would be on a seperate core, and the FPS wouldn't tank THAT bad, depending on your system (my processor had 8 logical cores, for example, meaning it theoretically can do 8 single threaded things at once, or a multithreaded program that has 8 threads, until it reaches over 8 threads, where it's going to delegate stuff to core 1 and up again, balancing the work load [if it's done well/right]).
Multithreading usually won't help those with single core processors, or in most cases, those with dual cores, since core 1 usually has to handle the OS.