My DD and I were trying to compare them when we rode EE, but it's really not possible. They are both great coasters, just different. I'd compare EE more to a really good Matterhorn and Mummy more to a really good Space Mt, but even those aren't good comparisons.
As far as the thrill factor, maybe the Mummy and EE are in the same ballpark, but one being an inside, dark ride and one on a big hill outside, they feel real different.