Let's forget about EA for a second
and think about the genre in itself.
The Sims is not the first life-simulation game, but certainly the most popular up until today (mostly because the competition died in the great simulatior crash long time ago).
This specific title profitted from its richness of content surrounding playing with the every-day life of your character(s).
You can create your own story, shape your own destiny, fool around and spend hours over hours just with the building system.
Keeping the strengths in mind, I believe a game of the same genre should represent these strengths aswell:
There should be an equally strong building system.
Since the competition is extremely strong in this one, I suggest not to drop the ball here.
Make a building system with a new approach or take them head on by making a similar system. In any case it shouldn't lack depth.
When it comes to the game mechanics surrounding the characters themselves, I believe there are many ways to create a very unique approach to the genre.
It could range from a pure single-character gameplay experience that has more depth to it and enhanced online-functionality (like actual multi-player), over to a fully indirect control of multiple characters. It could even be a game'ified Second-Life.
What you should keep in mind is that this is more than just a simulation. It's also a subtle form of RPG. The Sims may not have a classic RPG dialogue system, but everything else about character interaction screams "RPG".
One part will be that there has to be a challenge to the every-day life.
A second part will be that there has to be change to every day. Every day has to be unique. (which is why the 4Seasons add-on to Sims3 was a very important one)
But do not mix up change with individuality. Every NPC, every location, every occupation, every activity needs near infinite ammounts of variation.
There have to be hundreds of personality traits that shape hundreds of millions of personalities (like 4 traits each character, 100 traits to choose from ~= 100,000,000 variations).
If your character follows a carreer they need ranks, specializations, performance, happiness, colleague relationships, reputation, etc.
If your character does a side activity, there should be skill-levels to it, there should be ways to increase general stats, make them happy, sad, angry etc., everything has to come to life.
The focus about this genre is to follow a virtual living being through their life through everything.
If you manage to get the player attached to their characer(s), the game's going to be successful, because this is what the genre is about.
The genre is about immersion.