Sitefinity itself is a platform independent, because it is a .NET Application. So it can work on 32 or 64Bit .NET Framework. The oracle client is unmanaged code, which depends on the platform.
If you run the Sitefinity in 32Bit mode, you should use 32Bit Oracle client. In case you run the Sitefinity project in 64Bit mode, the Oracle Client should be 64Bit.
If the above is true for you, and you still get this error, could you please send us more information about the error. You can look into the Sitefinity.log file in the ~/App_Data folder for the detailed error stack trace.
the Telerik team