As others have said, emperor is the first "real" jump in difficulty because the AI starts with another settler (2 in total), which gives it a far bigger benefit than the gradual % based bonuses to yields have done up until king difficulty.
At emperor, you need to start taking your openings more seriously.
Openings can be compared to chess, in that you need to pay more attention to the viable choices you have early on, in order to secure a foothold in the game.
Up until king you can generally "freestyle" a lot more, since the AI generally has the same bonuses as you do, but is terrible at the game and thus you naturally crush them.
Not so much on emperor, thus you need to focus on openings more.
Your reply indicates to me that you are very reliant on dominating your neighbours early to create a snowball from all the free real estate that you're capturing, but that your peaceful play is lacking.
There is nothing wrong with prefering this path, but I make this inference because you should still be able to win peacefully regardless of whether or not you dominate your neighbour, but this obviously requires that you know how to make your cities productive in order to catch up with the AI (that is ahead in the early game due to the extra settler).
You got two main ways to improve your gameplay on emperor, and you should ideally try to incorporate elements of both in order to become a stronger player:
- You know how to spot an opportunity to attack the AI early, and you know how to execute it properly so that you dont fall behind.
- You know how to set up a strong cluster of self-settled cities with good infrastructure that will pay off, in order to secure a long term advantage even without rushing your AI neighbour.
For the first part, you already noticed that you cannot just "blind rush" an AI like you can on King difficulty.
The reason is that the AI gets more cities, which lets them produce more military units, and they get more science and production that lets them get walls up faster.
Both can kill off your early rush very hard.
You can still rush the AI on emperor, but you need to both spot and execute such a rush with more planning than on king.
This means that you no longer just pump out warriors and archers, but play accordingly.
You need to get units out quicker (I suggest getting 2-3 cities up really fast, and then pump out archers as those are excellent for taking out units and walls), but this is a risky strategy as you are essentially gambling on it paying off.
Thus if you want to do this more consistently, pick an OP civ to practice your skills first (Nubia, Gran Colombia and Gaul are excellent for this, especially the first two).
Also try to practice peaceful play more, where you aim to catch up to the AI by turn 100, without resorting to war.
If you can master both peaceful and aggressive play, you are ready for Immortal very soon, as the jump from Emperor to Immortal is not that big.
Deity is a different beast altogether since the AI starts with 3 settlers, and thus you need to refine your openings even more.
I have written about the very specific openers you can play in those cases elsewhere on this site (my most reliable being a 2 city religious opener with crusade), but I wouldnt worry too much about this yet since deity and emperor are quite different in terms of viable plans.
The key takeaway here is that the further "up" you go in difficulty, the less viable alternatives you have in order to win the game.
Where you can do basically whatever you want on Prince/King, Emperor and up restricts the number of viable paths, with Deity having the most narrow set of viable paths remaining.
Other than that its near impossible to give you specific tips on your gameplay, because on Emperor there are still tons of things you can do to improve your game, far too many to mention here.