This question already has an answer here:
- 32 bit or 64 bit OS on a 512 mb VPS? 3 answers
Does it make sense to replace a factory Win8 64-bit OS with a 32-bit one on a netbook-like Intel Celeron 847 laptop with 2GB non-extensible (soldered) RAM?
Yes, 2GB is really the minimum to run a 64Bit Windows and you don't have fun. Windows itself would use too much RAM. Everything under 3GB RAM should be 32Bit Windows.
Microsoft's system requirements for Windows 8 suggest that the 32bit version consumes significantly less RAM and HD space:
Aside from that, you're unlikely to notice the performance gains of a 64bit OS on a low end netbook.