Speed/Security? Why should we choose to use 64 bit instead of 32 bit?
Main advantages amd64 over i386
for more details look at wiki page.
What about performance?
Actually performance will grow up to 20-30% in general case. Its mainly due to intelligent compilers that can optimize even non-optimized code for new architecture (mainly due to SSE/SSE2 usage instead of FPU).
In many tools now you can use arithmetic operations while it was too expensive in 32bit system. For example your
The main problem is proprietary software. In case software developer spread their product only in binary for 32bit you may have a lot of problems. Sometimes it is possible to find workaround. And hopefully in the GNU/Linux world most of widely used software is open source.
The main benefit to 64-bit systems is the increased memory address space which is limited to 4GB with 32-bit systems.
This question on the Superuser SE might be helpful: 32-bit vs. 64-bit systems.
Also, here's an informal exploration of 32-vs-64 bit OSes on LifeHacker (though it focuses on Windows, much of it applies I think)
Some 64-bit programs, such as encoders, decoders and encryption software, can benefit greatly from 64-bit registers, while the performance of other programs, such as 3D graphics-oriented ones, remains unaffected when switching from a 32-bit to a 64-bit environment.