First, an update. I hope to play and post the next round sometime tonight.
Obsolete has voice concerns that the EE cannot hold up to a normal beaker economy. I don't have enough experience with the EE to really comment on this, but I do think that it is a strong game, and feasible at Emperor level. I'm not to the point yet of playing Immortal much, so I can't comment on that.
The EE gains a lot of strength mid/late game. After Communism, after building all the Espionage buildings, each city can have 20 base EPs from buildings plus a 100% bonus to EPs. Nationhood can add an additional 25% which may or may not be better than Vassalage or Bureaucracy.
I think what really gets the EE going though, is producing Great Spies for Scotland Yards. With a philisophical leader, by limiting non Spy GPP early, it doesn't take long to make a good amount of Great Spies. On normal speed, after CoL, run a single spy specialist in 3 cities, and in 50 turns, you will have 3 Great Spies (and well on the way to a 4th), and therefore 3 Scotland Yards.
Scotland Yard is a huge benefit. After Communism, one can easily expect to have 5 or more cities getting a 200% bonus to EPs plus 20 base EPs just from the buildings. This is a big difference from a beaker economy that will typically have one city with a 225% science bonus from library, university, academy, observatory, and Oxford. Other cities will be limited to 125% from Library, University, Observatory and Academy. With several good commerce cities, you can make a lot more EPs than you can beakers.
EPs are not the same in each game though. Sometimes, you have a tech-fiend with a city very near your capital that you can milk for techs for very few EPs. Sometimes the tech leader is far away giving a significant penalty. But having a religion's holy city, and spreading that religion to the target city gives a 40% decrease in EP spending. Whether you found a religion, or capture a holy city, this bonus is huge and worth pursuing.
Another benefit of the EE is fielding a huge army. Commerce tends to go to only gold and EPs, occassionally some to Culture during war to combat war weariness. Hammers do not have to be spent on libraries, universities, and observatories. Instead, they go to military. Big cities will generally always build markets and grocers just for the happy and health bonuses. These bonuses tend to go further in an EE because the % of commerce going to gold is generally higher than in beaker oriented games for 2 reasons. The first is that you tend to have a larger standing army, needing more gold for support, the second is that often you don't need all the EPs you could produce, and so store your commerce up in gold.
Because of generally having a huge gold surplus mid-game, an EE game allows building large armies of CR maces that are just waiting for an AI to research the techs for them to promote to Grenadiers or Riflemen. One can easily have 4000 gold saved up when the AI eventually gets Military Science, and promote 20 or so CR2 and CR3 maces to Grenadiers. Large #s plus superior promotions will roll over the AI that might have a slight tech lead.
Again, I am not saying the EE game is superior, just that it does have definite possibilities for a very strong and even superior game. It is not for every map or every situation. But in ideal cases, I think it has the possibility to be the strongest option, even at Immortal level and probably Deity as well.