Programmer here. A 64 bit chip allows you to run a 64 bit operating system, which is required for 64 bit versions of software.
A 64 bit version of any given piece of software is intrinsically going to differ from a 32 bit version in 2 key ways:
- It can access much more memory, which means it can hold a lot more information at once - providing that enough memory exists (ie. your computer has enough RAM)
- If all else is equal, it will tend to be slightly slower because the code and data is slightly bigger. (Each memory address is twice the size.) However, all else is not usually equal - as running a 32bit app on a 64 bit OS incurs its own (small) slowdown. Unless you are installing an OS purely for your DAW and need every last percentage point of speed, it doesn't matter.
For almost all purposes, point 1 outweighs point 2. Extra memory tends to speed things up, if you ever find yourself without enough of it.
However, Sonar is one of a very small number of apps that needs to host other programs inside it, ie. VSTs. If those VSTs are 32-bit, they can't be used directly with 64-bit Sonar, which is where Bitbridge comes in.
For a typical musician, if you have enough memory (over 4GB), and you don't have any 32-bit plugins that are essential to your workflow AND which are known to not work well (or at all) with Bitbridge, you should upgrade.
If you have 4GB or less, you'll see very little benefit, and maybe some problems. (But if you have 4GB or less, you won't be able to run memory-intensive samplers, which are probably the main thing that benefit from 64 bit systems.)