It is a while since I did my initial 737 sim, and bear in mind it tends to differ between companies. I did a full conversion onto the 737-700, then a differences course immediately afterwards onto the -300. There are normally anything between 7-10 4 hour sessions shared between 2 trainees. Also some of the sessions may be performed in a fixed base simulator. The first two or three sessions tend to concentrate on general handling and FMC work. You will practice steep turns, stalls, high speed runs, ILS approaches, non-precision approaches and also button down the preflight preparation. About the fourth session they may start introducing failures, possibly an engine failure (but probably already inflight) and then engine restart. Items to be covered from now until the final check will be rejected takeoff and evacuation, emergency descent, TCAS, windshear, GPWS manoeuvres and system failures. Basically they will try to cover most complex failures. Often you will complete the procedure for one system failure in real time, then be shown other system failures with the sim frozen just to cover all the other types of failure the system can have. For the final 4 sessions you will practice engine failures on takeoff, single eng approaches and go-around interspersed with other system failures. The final 2 sessions normally will cover the final check, which depending on country, will include preflight, taxi-out departure, airways, arrival and then non-precision approach. A takeoff with engine failure, single engine approach and go-around followed by single engine visual approach and landing. At some point a rejected takeoff and evacuation will be thrown in. Then a loft scenario will be flown which is a normal flight, in which a failure occurs. The crew then have to work the problem and bring the flight to a safe conclusion.
Basically the sim is a very good procedures training, the general handling characteristics of the sims can vary greatly from sim to sim, but as most important items are based around a decent instrument scan the feedback of the sim is not that important. In fact the worse the sim the easier it is then to fly the aircraft. The one thing that I believe no sims are good to recreate are landings. Although Base trg can now be done in the sim, and not in the aircraft, there is not enough visual perception to recreate the feel of doing a proper landing, and the sim cannot realistically recreate the atmospheric conditions. I hope this helps and is what you are after.