6u10 64-bit JRE and the 32-bit JRE installers both write files with the same name to %APPDATA%\Sun\Java\jre1.6.0_10
If both installs are launched near the same time, one may overwrite the other one's files.
Directory of C:\Documents and Settings\Administrator\Application Data\Sun\Java\
04/04/2008 12:31 PM 11,798,960 Data1.cab
04/04/2008 12:31 PM 506,880 jre1.6.0_10.msi