The airlines must like the fact the 777-300ER demonstrates more range than Boeing originally projected (7,500 nautical mile range in still air versus the original 7,200 nautical mile range estimate), not to mention the fact the 777-300ER offers a substantial LD3 cargo container capacity, which makes the plane even more profitable.
I think the 777-300ER may end up surpassing the 777-200ER as the best selling version of the 777. It has 85% to 90% of the passenger capacity of a 747-400ER and an even longer range. To put the range into perspective, a 777-300ER, which is 180 minutes ETOPS rated, can fly from Los Angeles to Melbourne Australia nonstop, the route which was the basis for QANTAS' 747-400ER requirement.
When compared to the 747-200, it has 90% to 95% of the passenger capacity, but at much lower operating costs, with much more range. This makes it a no-brainer as a 747-200 replacement. It also is a good fit for routes where the 747-300 or 747-400 is too large, or where the 777-200ER is too small.