Since they both provide vastly different experiences it's hard for me to really pick. Both are great attractions that I really love. Everest gives an entire beautiful area that is very scenic for the park while Mummy is smaller and indoors. The queues for both are fun, but Everest is more detailed. Ride wise though, while EE is fun , I do feel Mummy is better. The dark ride portion at the start is great for setting up more of the story and getting some good set pieces, and then has the thrilling ride despite no big drops and the fake ending is fantastic. EE is fun but despite being taller is less thrilling to me. Not sure what exactly but it has always felt like it is lacking something to me, especially at the top of the mountain. You get up the lift, then immediately have the backward section, don't really get to enjoy exploring the top of the mountain, and the backwards part is just a helix. And despite its size it really only has one main drop on it, otherwise it is just curves (granted a steep curve going back out of the mountain on the backside).
So overall I feel Everest is more about the scenery and beauty of the ride, and Mummy is more about the ride experience and thrills. They are pretty even overall to me for quality just in different areas, but if i had to pick just one to ride it would probably be Mummy since it is a more thrilling experience.