I think it's kind of pointless to try and draw conclusions based on what other people say they have heard about each the two games, and then use those second-hand impressions to draw comparisons between the two games.
It's silly to say that EiA has no economic component - there is a very important Economic Phase in which trade is taken into account, and not just European trade but overseas trade. However, it does not even approach the detail of CoG's system.
Having been playing CoG for a while now and EiA numerous times since I first got it almost 20 years ago, the fundamental difference is that CoG was designed from the ground up as a computer game, while EiA is a boardgame. (I have no idea what the EiA game will be like when released, so I reserve my comments to the board version.) The practical implication of this is that EiA makes a lot of compromises for playability's sake. For example, the economic phase only happens every quarter (March, June, September, and December turns). Why isn't the economy handled every turn? Probably for playability reasons - otherwise the game would take forever, given the number of calculations that have to be made (by the players) in that phase.
CoG is much more detailed in almost every way than the EiA boardgame. In CoG, every province produces different resources, has variable population, population consumes food and luxuries, etc. In EiA (boardgame), each province simply has a tax value and a manpower value. There is an "Economic Manipulation" rule that gives this a little variability, but it is an Optional rule, and is very simple and would appear extremely gamey to anyone expecting something along the lines of even CoG's slider bars. Rather than trading individual resources, trade in EiA is calculated simply by adding the trading values of all controlled ports. European trade is all considered to be done with Great Britain: GB gets the first (lower) trade value from each port, and the owner gets the second (higher) trade value from each controlled port.
This is a very elegant way of handling trade in a boardgame (go to war with Great Britain and you deny yourself income) but is nowhere near as detailed as the merchant fleets in CoG. Again, this is likely because in a boardgame, the players would have to handle everything, and making this system any more detailed would make the game take forever, and would also be drudgery as you sat and calculated every trade route possible on the map.
Combat in EiA is heavily morale-based, is influenced by tactical chit draws: I choose Assault, you choose Counterattack, and the cross-reference dictates that three rounds of combat will be fought at the 3-1/4-2/3-2 columns on the CRT. (Those actually are not odds - they're casualty and morale levels on the CRT.) The combat in EiA (boardgame) isn't nearly as detailed as even the CoG quick combat. You don't get any of the effects of unique unit subtypes - in fact, EiA doesn't make any distinction between light and heavy cavalry. It's all just "cavalry" for game purposes. Lancers? Forget it.
EiA was designed to be a playable strategic game of the Napoleonic Wars, with some operational flavor preserved. I think the designers did an incredible job - it really does manage to be playable, although you have to have seven dedicated players willing to get together regularly, knowing even a weekly game can take a year depending on how many turns you play in a sitting. However, a lot of the design considerations that went into EiA don't make sense in a computer game. In EiA there are two methods of calculating morale for a side in combat, the second of which is simplified because method one "almost certainly involves the use of a pocket calculator." You want to know what Method One is? It's just a weighted average of the morale levels of each strength point in the combat. That's something you assume without thinking in a computer game, but in a boardgame, requiring players to do long calculations between each battle gets very tedious very quickly.
I have no idea how the EiA (computer) designers are porting the boardgame. They may make a whole bunch of changes to take advantage of the computer format. But if the game gets ported directly as EiA the boardgame, it won't be anywhere near as detailed as CoG. CoG tries to be something of a sim, while EiA had to be a game, forst and foremost. The two design philosophies are almost diametrically opposed: in CoG you can't even get all the trade and income factors to add up at the end, while in EiA, you have to make the system so transparent that you can calculate every event in the game yourself. That's because in the boardgame, you had to do exactly that. So the system had to be simple enough that the transparency was replicable by all players.
There are a lot of similarities between the games: they're both province- (area-movement) based, corps-level games of the Napoleonic Wars, with a heavy diplomatic component. There are some very superficial differences: in EiA, the provinces have multiple areas, so while Berri (for example) has a tax value of 7 and a manpower value of 2, it is actually made up of four spaces with different terrain and forage values. In the end, the games try to model essentially the same things, but in every case, EiA had to take the choice of simplicity, because it was being run by players and not a computer. Every time you imagine how the games might compare, you have to take this into account before anything else.
One other point: in EiA, you could play smaller scenarios that skipped the Political and Economic Phases entirely: there were 1805, 1809, 1812, and 1813-14 scenarios that were simply about military manuevers, and played much more quickly. Thus, if you just wanted to play the invasion of Russia, you only used part of the map, and played from June 1812 to Feb 1813 (only nine turns). In this case, EiA just became a military game at the operational level. This was a function of the fact that in order to play a campaign game you needed 7 people. You could play the 1812 scenario with two. That's another difference between baordgame design and computer game design.