As already noted, you are using a 64-bit OS already. There are two advantages of switching to a 64-bit version of SQL Server and one disadvantage.
The sole disadvantage is that the 64-bit version of SQL Server will use 64-bit pointers. This means pointers will occupy twice as much memory, consume twice as much memory bandwidth, and so on. This is likely fairly negligible, but it is a disadvantage. It's partially compensated by the fact that switching to a 64-bit application will allow you to ditch the overhead of the compatibility layer 32-bit apps have to use to access a 64-bit OS's functions.
The major advantage is that numerous significant improvements were made in the CPU instruction set over time. Some of them were made along with the change to 64-bits and some of them were made previously.
But even for the ones made previously, the 32-bit build has to handle CPUs that don't have those features and to avoid the hassle of detection and switching between multiple instances, just doesn't use them even where they're present. For example, 64-bit CPUs must have SSE2, but 32-bit CPUs might not. So most 32-bit code just doesn't bother checking and assumes no SSE2. 64-bit code is assured SSE2 instructions are present and so will use it if it's the best option.
The biggest one is the increase in the number of named, general-purpose registers from 8 to 16. The number of 128-bit XMM registers was also doubled, from 8 to 16.
In addition, a 64-bit process can make use of large amounts of virtual memory. This is especially important with processes that access large amounts of structured data on disk. And, of course, they can use 64-bit integer operations which tend to improve the performance of encryption, compression, and even some filesystem operations on large filesystems.