Good points of Age of Empires III:
Good unit diversity: Each civ has a core of units semi-unique to them, making each one feel different enough that playing the Germans doesn't feel like a playing a reskin of the British, or vice versa. For the "European Civs" (I put that in quotes because while the Ottoman Turks are not from Europe at all, they play like one of the other European civs), that diversity is actually rather subtle, with each civ having one or two units totally unique to them, as well as a couple semi-universal units that are their "Best Units", which get special high-tier upgrades. For example, while the Spanish get Hussars, like the British, the British can upgrade them to "Kingsguard" Hussars, while the Spanish just get regular "Guard" Hussars. The distinction is rather intuitive; basically, if a unit gets a special name once it hits its second upgrade, it'll be better in some way than a unit that doesn't. In this way, the European civs harken back, somewhat, to Age of Empires II, which had each civ only have one or two unique units. On the other hand, each of the Native American and Asian civs are completely different, with entirely different units and even different mechanics, and which units each civ is best with is fairly obvious a few minutes into playing them. The diversity is further enhanced with mercenary units available from the home city and native american units from trading posts.
Good story campaigns: I can't quite make this point without clarification. The first three campaigns were not that great. Those were the pre-expansion ones, and frankly, the series had really stopped working out those storytelling muscles it had in Age of Empires II. The action often felt disjointed and rushed, with the endings of each of the three campaigns being the only bits that seemed to matter or have any impact. However, all of that said, the latter five campaigns were actually quite good, especially if you could disengage them from the taint of their predecessors in terms of tropes and pacing. In addition, the characters personal struggles in the latter five campaigns were more apparent, their inner struggles seemed to mean so much more. Really, if you want a great story, the latter five campaigns are pretty damn good.
Good* Mechanics: This game has some rather... mixed mechanics. I'll get to the bad later, but for now, the good news! The home city is the big thing that was touted on release, and frankly, I like the concept a lot. It allows a player to gain advantages specific to their strategy, whether it be resource gathering, naval dominance, or raw military power. Essentially, the way the Home City works is that the player assigns cards to a deck, each card representing a batch of units or an upgrade or some resources. When a home city shipment is available in game, the player selects one of the cards they've assigned, and after a brief waiting period (Hey, it takes time to get a Declaration to Claim the New World overseas. Cut them some slack.), the units, tech, etc. arrives. In addition to this as one of the primary mechanics, you've got your normal suite of resource gathering (done with villager-type units) and military unit production. An interesting nuance of the unit production here is that when you've got a military building selected, let's say, the Barracks, and let's say you want to train a sqaud of Musketeers. You can shift-click the unit portrait to train five at once. While this may not seem novel by itself; a few games already allow this sort of thing, the novel thing is that doing it this way makes the waiting period for your units slightly longer, but you get all five units at once. The Russians and Chinese have this as their primary mechanic, with the Russians training "blocks" of infantry, and the Chinese creating "Banner Armies" which are groups of various unit combinations. Overall, the mechanics are decent in most respects. In addition, the game very cleverly and subtley hampers rushing, which was a brutal, and often severely effective tactic in Age of Empires II, by making it so that the player cannot send units from the home city, or even train them, until the second technological era. I hardly ever notice that my efforts at building an army are being hampered by this restriction, but when I do notice it, I am appreciative of the clever design choice.
Bad points of Age of Empires III:
Bad* Mechanics: As I said, this game has some mixed mechanics. Now we come to the bad. The primary problem we have here is that while the home city, is in concept, a nice idea with some potential for strategic use, it seems best used as a rush enabler. Earlier, I mentioned that the game restricts rushing by limiting military units to the second age and following. But the home city can easily be stocked with military unit shipments so that come second era, you can get an entire army, virtually free of charge. Here's a hot tip for those cheese players out there: Get the best second-era military unit shipments you can. Then, in game, save up your shipments. Once you get to age II, build a Church. Then research Mercantilism, which gets you around 3 shipments for 1,000 Coin. Then, in essence, spawn a horde of troops. Admittedly, this really only works for the European civs, but the overwhelming potential for early-midgame rush is still somewhat staggering, and it means that some of the more interesting home city shipments may not ever see play. In addition, many games, it seems, are decided well before the final technological era. The reasons for this are two-fold: A) Reaching that final era and researching all the upgrades is simply prohibitively expensive, and B) It just makes more sense to strike your enemy before then, fatally, if possible. This makes the late-game content feel a little unnecessary, as you're probably already winning if you can research that final era, and if you're not winning, spending 4,000 food and coin isn't going to make things that much better. The game does mitigate this somewhat, by having a "Revolution" feature, an alternative to the final age-up, which turns all your villager-type units into militia-type units, and also gives you a plethora of new military options for your civ. However, if you're far ahead enough that you can forgo economy entirely, than you probably don't need the feature anyway. Also, it's only available to European civs, so the final age cost problem is still relevant to Asian and Native American civs. Also, unit counters and stats can be difficult to wrap one's head around, as the developers saw fit to give the player the literal math used to determine unit stats. For example, I believe the movement speed for the average footsoldier was 7.25. Not 7, not 8, but a fraction, 7.25. While this may not seem like a major issue, throwing numbers like that at a player makes the game feel less than polished, and also degrades the meaning of the numbers themselves. 7.25 what? And what does it mean when my Musketeer deals 8 damage, but the Hussar it's attacking has 0.20 armor? Does it deflect 0.20 damage? Or 20% damage? The game doesn't tell you, meaning you'll have to examine the numbers closely to determine exact impact of your units against your opponents.
Anachronism: While I will be the first to admit that anachronism in a strategy game isn't that huge an issue, and is in fact, almost to be expected in these kinds of games, the situation here is rather glaring. Granted, the problem is bigger in the first three story campaigns, and I wouldn't mind it quite so much if it were restricted to the game itself only. But c'mon. Having Revolutionary War era musketeers accompany Amelia Black, a railroad owner? And having them in full garb in cutscene? That's the sort of thing that stretches disbelief to the breaking point, and was one of the reasons that those campaigns did not match the quality of the latter five.
Overall Review: It's pretty good. Steam's char. limits are ♥♥♥.