SQL Server 2008 R2 MERGE statement to replace single INSERT AND UPDATE statement combined
I haven't done any comparative testing of the two (yet) nor seen any articles on the topic. There is an Optimizing MERGE Statement Performance article on Technet but this doesn't include any comparisons with the update/insert syntax.

I can however suggest an improvement over your original syntax which eliminates the IF EXISTS lookup:

UPDATE 
    dbo.tblCustomer
SET 
    CustomerName = @CustomerName
WHERE
    CustomerID = @CustomerID;

IF (@@ROWCOUNT = 1)
BEGIN
    SELECT @New_ID = @CustomerID;
END
ELSE
BEGIN
    INSERT 
        dbo.tblCustomer
        (Taalnaam)
    VALUES
        (@CustomerName);

    SELECT @New_ID = SCOPE_IDENTITY();
END


You may also be interested in Mythbusting: Concurrent Update/Insert Solutions, which includes some examples of MERGE usage.