Just reaffirming what others have said (and I don't care for drops!). The track on Space Mountain is fairly tame, but since it is in the dark, it really does a number on some people. If you listen to the soundtrack, it will let you know what to expect. (There are a few small dips, but nothing bad (less stomach-jarring than Pirates of the Caribbean, IMO) and like I said, the soundtrack warns you.)
I think the new cars will probably make the Matterhorn smoother. (And yes, SilentFeline, if you were in one of the old cars alone, there was WAY too much room and it was kind of uncomfortable!) The only other possible problem I can think of for the Matterhorn is if you are deathly afraid of heights...but I'm afraid of heights and I'm OK on it. The drops are minimal.