There are many differences in gameplay between the two games. I don't have Generations or the newly-released Showtime expansion packs, nor most of the stuff packs, but the main differences should still be the same between the games.
Open-World
The main difference is the open-world characteristic of The Sims 3. Unlike in the two previous games, your are not restricted to your home lot and there is no load screen when you wish to go to a community lot. You can peruse at your convenience all the details of your neighborhood, visit neighbors' houses or walk by the beach. Your Sims can own bicycles or cars to use to move around town, or they can walk, run or take a cab for free. With the World Adventures expansion, you will be able to visit three foreign countries and open-world applies there too, with only a loading screen where you would technically have a flight.
Professions
The Ambitions expansion pack will give you the possibility of pursuing a Profession track. Unlike with regular jobs, you can follow your Sim while they're working and influence how they perform. For example, you may have to tell your Sim to put out flames on a house as a firefighter and break down doors to save other Sims.
In addition to careers and professions, Sims can be registered as self-employed. Self-employed Sims can be writers, painters, inventor and anglers, among others, and can work on their own schedule and still have things analog to promotions. You do not need the Ambition expansion to have the self-employed option, and you can still make money off writing books or painting even if your Sim is not registered as a writer or painter.
New Skills
There are also new skills to master in The Sims 3 as well as things to collect. There are a lot of never-seen-before skills such as photography, martial arts, sculpting, horseback riding, various instrument playing and others. You can also collect rocks and gems, bugs, seeds and fishes.
Lifetime Rewards
The fears mechanism of the Sims 2 disappears, but the wishes have stayed. Sims can have four regular wishes promised as well as a lifetime wish, which usually is influenced by their personality and can be career or life based, but you can choose from the dozens of available wishes, ranging from Gold Digger to Jack of all Trades. Fulfilling those wishes gives your Sims points which can be used to buy lifetime rewards, which can be objects like in the Sims 2, but are usually characteristics or bonuses that your Sim gains, such as a Steel Bladder or no bills forever. Pets can also have four regular wishes promised and lifetime rewards.
Opportunities
In The Sims 3, your Sims can have opportunities to do various more-or-less random things for boosts. A sim can have up to three opportunities at a given time, one career-based, one skill-based and one miscellaneous. These opportunities may have a time frame for their completion and as a reward, a Sim can gain Simoleons, a career boost, a skill boost, a relationship boost or a celebrity level boost.
Customization
Customization has been taken to a whole new level in the Sims 3. You can customize just about anything you want any way you want. Many aspects of Sims can be customized such as body weight, muscular mass, muscle definition, body hair, tattoos, hair highlights/roots/tips, skin color, voice pitch and personality traits. An adult Sim can have up to five personality traits. Traits can be mental, physical, social or lifestyle. There are also hidden traits which can be acquired by doing different things. Pets can have up to three given traits, but they can also be trained into new traits like Neat or Playful, so they can have more than three traits.
You can also edit your neighborhood, community buildings, parks, houses and apartments. You can also customize clothes and furniture colors, textures and prints. You can build fountains or have a pool on your roof.
As for the casual/complexity question, I would say that The Sims 3 retains the complexity from The Sims 2, and even adds a bit to it since you can retain control of your Sims even when they're at work if they have a profession. So in that sense, you don't just send your Sim to work for hours and have them out of your way.
Those are the big things I can think of for the moment. I'll edit if I think of other things.
Best Answer
First of all they will do whatever is needed to fulfill their needs, then the main things that sims do are: play on the computer (if they have one), prepare food (even if they're not hungry) and interact with other sims on the lot; those are the ones they do most. But they can also read a book (if they have bookworm trait they will do this more often), play an instrument (if they have the skill), kleptomaniacs will steal stuff, kids and teens do their homework (they will do it on their first chance if they have some nerdy trait, but if they are rebel they will never do it on their own), adults will go to work on time (though, they will not look for one, you have to choose it), they may ask other sims to marry if their relationship is good enough and they like him/her too... stuff like that.
You may want to take a look at this page: http://sims.wikia.com/wiki/Free_will