Your application may or may not run faster. I've seen improvements for some applications but not others. It depends on how much your application takes advantage of 64 bit (math) operations and if this offsets the larger data and code that x64 uses and therefore has to load into instruction and data cache before it can be executed.
Link
This is worth a read. It's old (.NET 2.0) but much still applies; pointer sizes, COM interop etc:
Migrating 32-bit Managed Code to 64-bit
It's also worth knowing that even on x64 the CLR has a single object size restriction of 2Gb. This isn't an issue for 99% of scenarios but if you're moving to x64 presumably it's because you might be working with large data sets. See here for more discussion:
Are C# Strings (and other .NET API's) limited to 2GB in size?
So. Unless your application uses data that doesn't fit into 32 bit memory or makes heavy use of 64 bit operations you may not see much, if any improvement.
The other downside is that Visual Studio for x64 applications has some limitations:
Edit and Continue is not available
for 64-bit debugging.
You cannot debug in mixed-mode, calls
from native code to managed code, or
vice versa, in 64-bit code.
See: http://msdn.microsoft.com/en-us/library/ms184681(VS.80).aspx
Note: The 64 bit C++ compilers aren't installed by default. You have to select them during the install.
I also just found this (because I'm optimising a x64 application myself).
"Porting and Optimizing Applications on 64-bit Windows for AMD64 ..."
http://download.microsoft.com/download/5/b/5/5b5bec17-ea71-4653-9539-204a672f11cf/AMD64_PortApp.doc
Has lots of good pointers on compiler switches and the like.