32bit vs 64bit
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64bit refers to how big memory can be accessed. That is, each address is stored as a 64bit value. It has nothing to do with how big numbers you can do computation on. For example, SSE handles 128bit data and AVX handles 256bit data.
[edit] Memory Capacity
32bit Addresses can locate less memory than 64bit. 2^32 bit = 4,294,967,296 bit = 4 billion memory cells (bytes) = 4GB. 2^64 bit = 18,446,744,073,709,551,616 bit = a very big number of bits = 16 Exabytes are addressable.
[edit] Speed
The main performance improvement comes from x86-based processors supporting more registers in 64-bit mode than in 32-bit mode.
[edit] Compiled Executable Size
64-bit executables are usually larger due to the size of pointers (64 bits vs 32 bits, hence 2 times larger). In my experience, the actual difference is about 1.25 to 1.8 times larger for 64-bit executables
