64 vs 32 bit refers to the instruction set of your processor. 64 bit instructions are 2 times as wide as 32 bit instructions, which allows for more complexity and more address space.
Almost every modern 64 bit processor also implements the 32 bit instruction set. Intel and other manufacturers do this to ease the transition between architectures. It is also a very simple thing for intel to do, since 32 bit instructions can run on 64 bit hardware with almost no modification. 64 bit instructions cannot run on 32 bit hardware, however; the hardware simply isn't built for it.
Mac OS X and several versions of Linux use a kernel that runs in 64 bit mode, while maintaining compatibility for 32 bit applications. This is possible because both instructions sets are implemented on the CPU, so there is no translation occurring; this is NOT like using Rosetta to run PPC applications on an intel Mac. The only performance hit is that 32 bit applications will take up slightly more memory running on a 64 bit system, and you can see why: a 32 bit instruction running on a 64 bit chip 'wastes' up to 32 words. And while this seems dramatic, you should know that there are optimizations in place to prevent the extraneous memory footprint from being too bad.
So, what are the benefits of running the strict 64 bit mode? Nominal, unless EVERYTHING you run is 64 bit compatible. If you attempt to run 32 bit applications in this mode, they won't work.
What are the downsides of running the default OS X kernel (which IS 64 bit, with 32 bit compatibility)? None that you will notice. If an application is built for 64 bit architecture, It will run with 64 bit instructions and be able to address as much memory as is available. If it is built for 32 bit only, it will use 32 bit instructions and be limited to addressing 4GB of memory. This operation is largely transparent, as most applications are distributed with compiled versions for 32 and 64 bit in a single package; your system will run the correct version based on the system's capability.
Will applications benefit from 64 bit? Absolutely, IF the developer optimizes and compiles them to use 64 bit. Don't be confused about this point, you can't make your system perform better by forcing it into 64 bit mode if your applications aren't built for it.