Unfortunately, there are very few routes that involve ETOPS restricted zones or the poles. The only areas where the A340-500 may have an advantage over the 777-200LR are routes near the West coast of South America and trans-Antarctic routes. It should also be noted that on most other routes, the 777 outperforms the A340- for instance, CI was unhappy that their A343 was unable to make JFK to TPE nonstop, so it has to make a stop in Anchorage. One reason why CI was contemplating buying 777's and having Boeing buy back their A340s was that the 777 does have the range capability to do JFK-TPE nonstop.
And I highly doubt that anyone who has read any of your previous posts will agree that your "comparisons" between A340 and the 777 are "objective."