Either JDBC or ADO.NET works just fine. Oracle's JDBC drivers are really good; so are the ADO.NET drivers. Do your best to obtain the latest driver versions that are compatible with your server. Your choice (JDBC/ADO.NET) should be dictated by the implementation technology of the rest of your client software. If you're building a dot Net (in a Visual Studio environment) app use ADO.NET. If you're building a Java client (e.g. in Eclipse) use JDBC.
Where you will run into performance trouble is if you try to build a heterogeneous client, trying to use software gaffer tape to attach JDBC to a C++ program, or ADO.NET to a Java program. That will be slower and more unstable. For example Crystal Reports claims to be able to use JDBC data connectors, but they have an inefficient adapter between their native code and Java.