Okay, so I haven't actually finished a game yet; I've gotten to 1663 on an Savoy to Italy game, I've gotten to 1600 on a Crusader Kings 2 converted game where I created Finnish North America, and I've gotten to 1670 on an Omani game. I haven't gotten to the revolutionary part yet, or the colonial uprising part, but I know it hasn't changed much from EU3 so whatevs.
So, if you're not actually sure what this game is, it's a grand strategy game. It starts in the year of our lord 1444, and ends in 1821. This means it's involved with colonization, the reformation, etc.. You can be a heavy trade nation, you can be a heavy colonizer, you could just conquer all of Europe (and the world) if that's your fancy.
Monarch points are the newest feature in EU4, and they're very interesting. Each monarch has stats, that go from 0 to 6. You can get advisors that will help, but generally your power is tied to the monarch for the most part. Your monarch points are separated into Administrative, Diplomatic, and Military. Each of these points can do multiple things; Admin points help you core provinces (basically coring means it becomes a part of your nation fully), Diplomatic points are used while doing peace deals (higher cost peace deals require more diplo points), Military points can get you admirals and generals, and they can all be used to upgrade your technology. Technology is generally what you want to concern yourself with the most, but these points can also give you ideas.
Ideas are another new feature. They were in EU3, but they were very different. Starting from Admin level 7, you can pick an idea group from each of the three monarch point groups. Each of these groups has 8 (or 7) ideas, and once you get them all you get a bonus idea that is quite powerful. These will help you to guide your nation into what kind of game you want; if you're a colonizer, you would pick the exploration and expansion mode. If you want to conquer everyone, then pick one of the military ideas. If you're a trade nation... pick the trade idea group. There are also national ideas, which unlock for every third idea. Most of these ideas try to guide a nation into a specific role; in my Omani game, they pushed me towards a trade game, and in my Savoy game they pushed me towards a diplomatic one. They're generally helpful even if you don't play the way you're supposed to, though.
Trade is another feature that's been massively overhauled. In EU3 it was mindless button clicking but here it's more intricate while also being simpler. Each province has a specific node that the trade is coming to... not that you get more by having that province, but it wouldn't hurt; those provinces are generally pretty great. This trade will either be collected there or be forwarded to a new node. You generally want to collect from nodes you have a majority of provinces in and forward towards those nodes if you have any more. it's also very potent; I was pretty strapped for cash at all times in my Italian game at my military force limit, but in my Omani game I'm at my force limit, have 3 level 2 advisors, and I'm still making mad bank.
The military game hasn't changed much, but it didn't really need to. You have multiple modifiers that can be improved. Morale gives your troops longer staying power in a battle, Discipline gives you more deadly troops, your military tech level can give you more deadly troops. They did improve war by adding the ticking war score; if you go to war to get, say, Armenia, if the enemy has Armenia the score will tick up in his favor. If you capture it, the score ticks up in YOUR favor. The feature was in CK2 and Victoria 2 but it's nice to see it here as well.
The game has more events than EU3 did, and it does help it give more flavor, but it's still mostly freeform. You can have any number of weird things happen; in my Omani game, Scotland won the war and created Great Britain. and then England revolted, and then Scotland won it AGAIN. Siberia hasn't even begun to be colonized because Muscowy has been fucked up by many many many things. Portugal and France have been in a personal union for 70 years at this point (A personal union is one ruler, The De Avis of Portugal in this example, ruling over France). They're never gonna inherit France, cause it's too big, but they've been the big players in Europe because of it. Spain is colonizing Brazil while Portugal is colonizing everywhere else in south america (the opposite of what happened in real life). It's just fun to see what kinda crazy shit happens.
I mean, they have a score screen which is new, but it's worthless; it's fun to see, though! It's seperated into the three monarch point things, and there are multiple things that go into each rating; tech level, provinces, ideas, etc.
There are still problems in the game, of course. It's pretty buggy at the moment; nothing that's going to kill the game or anything, but some events and shit are wonky (Japan gets catholic rebels a lot, for example). There are some balancing stuff they need to do too. The ironman mode (cannot reload) is also really wonky for me right now.
but you know what? I've played this game a lot since it came out and I'm going to play it more and it's just magical. So eff it.