While the memory used by strings and floating point data generally won't change in size, integers and pointers are now twice as big as they used to be, and perl makes use of a lot of integers and pointers internally. Going to a 64 bit architecture also means that the way some data structures are packed together changes and makes them a bit bigger on top of the extra memory needed for the larger pointers and integers.
This is true of any language, not just perl. Do a 64-bit build of python or ruby, or recompile your C program to be fully 64-bit, and you'll see the same sort of memory usage increase.
Basically assume a move to a 64 bit platform means you need twice as much memory on the system for equivalent performance. That's a bit of an over-estimate, but it should see you through OK, and memory's reasonably cheap.