People often reference the "big drop" on Everest as an element that would make it "scary" to people. In truth, the drop on Everest is simply not the same sensation as the types of drops that usually scare people. The little drops on Space Mountain are actually more intense in terms of giving you the sensation of falling. The drop on Everest goes almost immediately into a banked turn, which all but eliminates that "falling" sensation that usually makes a drop thrilling to many people. So if drops are what scare you, don't even be concerned about Everest. It's not the same type of drop. The drop on Splash Mt, for example, is about 30 feet shorter and is much more intense than the Everest drop. So are the ones on Space Mt, which are only a few feet each.
As another poster said, it depends on what scares YOU personally. If it's drops, then we've covered that (not an issue on Everest or the Mummy). If being in the dark is what scares you, then all three have that element, but it's considerably less so on Everest. If going backwards is what scares you, then Everest is the worst for that. The Mummy does it, but only for a few seconds, and it's not going fast at the time. In actuality, the Mummy is very much like Space Mt at two points in the ride, only it's a MUCH smoother ride.
If intense special effects are what scare you, then avoid the Mummy at all costs. It is loaded with them. It has fire, bugs, things jumping out at you, and a few other surprises. Everest doesn't really have any impressive effects to speak of. The Yeti is cool, but blink and you'll miss it. You only see it once during the entire ride and it's way too brief (I think Disney really missed the target on that one). Someone mentioned the impressive Mummy animatronic. It IS impressive and you actually get to see it for more than half a second. You're not even going fast yet when it makes it's appearance.
Hope that helps!