How to properly close ODP.net connection : dispose() or close()?

It looks like everybody else, I noticed late that you're in powershell. In that case, it doesn't really matter. Everything is going to get cleaned up when the shell ends regardless. I suppose you could add a [catch] and maybe close/dispose the connection there if it's still open, but I think that would only be necessary if you planned on letting your script continue.

I'll leave my longwinded c# answer below. Even though it doesn't really apply to your script, it explains the difference (or lack thereof).

The short answer (for c#):

using (var conn = new OracleConnection(connectionString))
{
}

"using" ensures that .Dispose is called at the end of the block even if an exception is thrown. That way you never risk a connection being orphaned until garbage collection finally gets around to cleaning it up and that might be well after you run out of database connections.

The long answer:

Using a reflector, you will see that Dispose calls Close:

protected override void Dispose(bool disposing)
{
  if (ProviderConfig.m_bTraceLevelPublic)
    Trace.Write(OracleTraceLevel.Public, OracleTraceTag.Entry);
  this.m_disposed = true;
  this.m_dataSource = string.Empty;
  this.m_serverVersion = string.Empty;
  try
  {
    bool flag = this.m_connectionState == ConnectionState.Closed && this.m_oracleConnectionImpl == null;
    try
    {
      if (!disposing)
      {
        if (!flag)
        {
          if (OraclePool.m_bPerfNumberOfReclaimedConnections)
            OraclePool.PerformanceCounterIncrement(OraclePerfParams.CounterIndex.NumberOfReclaimedConnections, this.m_oracleConnectionImpl, this.m_oracleConnectionImpl.m_cp);
        }
      }
    }
    catch (Exception ex)
    {
      if (ProviderConfig.m_bTraceLevelPublic)
        Trace.Write(OracleTraceLevel.Public, OracleTraceTag.Error, ex.ToString());
    }
    if (!flag)
    {
      try
      {
        this.Close();
      }
      catch (Exception ex)
      {
        if (ProviderConfig.m_bTraceLevelPublic)
          Trace.Write(OracleTraceLevel.Public, OracleTraceTag.Error, ex.ToString());
      }
    }
    try
    {
      base.Dispose(disposing);
    }
    catch (Exception ex)
    {
      if (ProviderConfig.m_bTraceLevelPublic)
        Trace.Write(OracleTraceLevel.Public, OracleTraceTag.Error, ex.ToString());
    }
    try
    {
      GC.SuppressFinalize((object) this);
    }
    catch (Exception ex)
    {
      if (!ProviderConfig.m_bTraceLevelPublic)
        return;
      Trace.Write(OracleTraceLevel.Public, OracleTraceTag.Error, ex.ToString());
    }
  }
  catch (Exception ex)
  {
    if (!ProviderConfig.m_bTraceLevelPublic)
      return;
    Trace.Write(OracleTraceLevel.Public, OracleTraceTag.Error, ex.ToString());
  }
  finally
  {
    if (ProviderConfig.m_bTraceLevelPublic)
      Trace.Write(OracleTraceLevel.Public, OracleTraceTag.Exit);
  }
}

Is there any real difference? No - the unmanaged resource IS the connection which is taken care of with .Close. You'd see no functional difference (other than delayed tracing) if you checked the connection status in a finally block and called .Close there if it was still open.

  OracleConnection conn = null;
  try
  {
    conn = new OracleConnection(connectionString);
  }
  finally
  {
    if(conn.State != ConnectionState.Closed)
      conn.Close();
  }

That said the recommended pattern for idisposible objects is to use a "using" block. Yes I suppose it is true that you have the option to reopen the connection with close, but I don't see that being a useful thing to do.

If you didn't use a using or a finally and an exception is thrown and close/dispose is never called, then freeing the connection to the db would be nondeterministic - Dispose(false) would happen whenever the garbage collector got around to it - and that might be long after you run out of connections to your db.

    OracleConnection conn = null;
    conn = new OracleConnection(connectionString);
    conn.Open();

    //exception occurs - Close is never called - resource leak!!

    conn.Close();