As Flieger said, the flight and ground spoilers are different, but in general, the 737 doesn't really have any great pitch up tendency.
It touches down nicely, then requires some (but not excessive) backstick to keep the nose from just falling to the runway. Relaxing the back pressure is enough to lower the nose to the deck without too much difficulty.
However, there are a couple of things that are probably worth mentioning that I don't think I've seen yet.
1. Autobrakes change the equation somewhat. Autobrakes, unlike manual braking, will activate with main wheel spin up IIRC. This definitely will have the tendency to pitch the nose down, especially MAX autobrakes. If you aren't ready for it, it will snatch the nose down pretty dramatically and you need to catch it as soon as it tries to do that.
2. You don't really full stall a transport category airplane onto the runway like a utility plane. Instead you more or less fly it on before you reach stall. One of the reasons is that the main gear is behind the center of rotation. So, if you are sitting ten feet above the runway slowing to a "conventional" landing, as you raise the nose, you are driving the mains into the dirt which, with a little settle actually makes for a harder landing. Instead, you would ideally almost stop your rate of descent, then lower the nose very slightly and actually rotate the mains up as you touchdown. This is obviously something of an art and I am not at all sure if it is represented very well in FSX.
3. The importance of proper airspeed has already been emphasized here. Another reason that you don't want to either come in too slow or allow yourself to get too slow on landing is that at some point you will have insufficient airspeed over the elevators to provide any nose authority. In other words, if you come in dragging it over the fence and holding your nose up for too long after touchdown, your nose will eventually drop...just not at a rate that you have any control over.
Deacon