Which is Better - 32 or 64 Bits?
If you are doing heavy work where you have started to hit the 4GB memory barrier, then 64-bit is for you. Certain intensive tasks such as encoding video or audio also run significantly faster on 64-bit operating systems (NOTE: this is implementation specific).
Phoronix has done some testing
(2009), comparing 32bit/PAE/64bit, and this seems to indicate that 64bit performs better than 32bit in almost all cases.
Early 64-bit adopters were plagued by incompatibility problems (most noticeably Java and Flash), however most issues have now been resolved.
Some applications such as Flash do run slower in 64-bit mode, however work continues to improve on this.
Other platforms which also come in 32 and 64-bit flavours may experience more problems especially due to a lack of 64-bit device drivers as incompatible user application. As Ubuntu is entirely open source, this is not the case as all hardware supported by Ubuntu works equally well in 32-bit and 64-bit environments. The same applies to open source user applications as well.
Which Should I Choose?
Unless you have specific reasons to choose 32-bit, we recommend 64-bit to utilise the full capacity of your hardware.