Two Oracle clients on the same server
You should not install more than one Oracle Client (per architecture) on one machine. For sure they do not work in parallel. 

By heart I know several issues:

You would have to change PATH settings in order to determine which Client you want to use. TNS_ADMIN environment variable is used by both versions and must be set accordingly. Oracle OleDB provider can be installed only once (per architecture). Version of Oracle Data Provider for .NET (ODP.NET) must match the client version. Using ODBC can be also a challenge.