When I think about it, I feel the original AOE3 is a combination of some sharply contradictory design directions, either aiming at more fun and diversity, or competitive pvp. Some may be the result of technical limitations but ended up with these weird combinations in the final product.
For example, the card unlocking system may end up being unpopular, but it seems to me like one that tries to appeal to casual players, so that they stay around longer grinding the game. Yet it could work really great in campaigns.
Native settlement is another thing. I could hardly imagine it being designed as a good competitive pvp option. Maybe that’s a pure retrospect and the developers had pvp in mind when designing them, but I don’t know.
The home city screen looks awesome and can be further customized with all kinds of aesthetics, which you rarely stare at in a competitive game (and now you even want to minimize it 
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Diverse biomes and map objects, which serve little gameplay purpose.
More characteristics for the AI players (AOE4 still has “hard AI” as AI player name).
But now there are things that go in the opposite direction:
1. Campaigns: I would not say they are bad but…mediocre. And the number is small. Surprisingly, AOE2 also only had three campaigns (not counting the tutorial) at launch, but three different campaigns in totally different settings feel grander than three acts of family history. The missions are rather shorter and linear as well. Later expansions still did not offer more and better sp content. I have written a post talking about campaigns specifically:
2. Map sizes: before DE, large map options are restricted to a very small number of maps. All others are automatically adjusted according to player numbers. It encourages fiercer early battles and competitions for map control, but if I want to sit around playing a “grander” battle or just build large cities, I cannot. AOE2 has map size options independent of the player numbers, and if one wants to play competitively, there can always be a “standard” option.
3. Game modes: IIRC vanilla AOE2 also had few game modes but a lot was added in The Conquerors. Original AOE3 only had two modes and a few more were added as late as TAD, including regicide (only one map) and king of the hill. I know none of the game modes are as popular as standard, but it would not hurt to have the option in case people get bored some day and want to try something else (for example, I never liked Total War’s decision of removing naval battles just because most people autoresolve them. What if I suddenly want to play one?). It’s probably a compromise due to limited resources, but the decision of removing these contents in favor of others seems to me a result of greater emphasis on competitive pvp.
Overall it feels like a combination of more diverse and radical designs that tried to break away from the long-established, dull esports formula, and also an attempt to catch up with the ongoing esports trend at that time.
Don’t get me wrong. I have been enjoying the game a lot. I just feel it has so much potential that is not fully utilized. It’s really a pity. I hope future updates could learn from what worked and what didn’t.