Use Oracle 64-bit if your SGA requires a size > 4GB. Otherwise, stick with the 32-bit version. As jdorlon suggested, each is a seperate piece of software. Typically, the 64-bit version is behind the 32-bit version for new releases and bug fixes.
Is it also dependant on the application. This is my result set.. With what you mean is ORCL sells 32 bit and 64 bit seperately.
SQL> select * from v$version;
BANNER
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Oracle7 Server Release 7.3.3.3.0 - Production Release
PL/SQL Release 2.3.3.3.0 - Production
CORE Version 3.5.3.1.0 - Production
TNS for IBM/AIX RISC System/6000: Version 2.3.3.0.0 - Production
NLSRTL Version 3.2.3.0.0 - Production
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