The compiler, won't make a difference once you get to run-time. Java compiles to a bytecode, and the output is independent of the architecture used to run the compiler.
You may see different compilation times between a 32-bit compiler and a 64-bit compiler, just like you may see different run times between 32-bit and 64-bit runtimes (but runtimes go under the JRE, not JDK). This depends on how well they have been optimized for that architecture (x86/x64), but one does not affect the other (a slow compilation doesn't have to mean the execution will be slow, or vice versa).
(Of course, this assumes that the two compilers only differ in bitness, and that they aren't applying different sets of optimizations or otherwise do some things slightly differently.)