If its mostly adults, I would say EPCOT
If its mostly kids, I would say AK
Though I would say both if possible!
If you are there for four days, you might as well just "do it" and go to all four parks each day. You will have plenty of time to relax on the cruise ship and the day you go to AK can also be a relaxing day due to the park usuallly closing early.
Also, if you are staying at a Disney resort, take advantage of Magical Hours that lets you in the park earlier or stay later on certain nights!
Epcot, on the other hand, is essentially a permanent world's fair. The offerings here are geared for an older audience and includes a healthy dose of information in every exhibit. While there are some thrills to be found, the emphasis is much more on enlightening while entertaining. There are definitely more things to do at Epcot, which will almost always take more than a day to see everything.
I've taken my boys to EPCOT since they were toddlers and they have always loved it. I've never understood why people think it's for older kids, but I guess it depends on the child.
However, AK is very chill and relaxing. There are thrill rides hidden among lots of relaxing animal treks. AK is also a lot of walking. I enjoy AK quite a bit but have never been able to spend an entire day here. Also, they close early in the day so there are no fireworks or shows to end your night with.
Epcot has many more rides and I would consider it a 3/4 day park. With rides like Soarin', Mission Space, Test Track, and then some of the slower rides like Journey into Imagination, Spaceship Earth, Nemo, Turtle Talk, and Innoventions (Sum of all Fears is a favorite of mine), there is much more to do. And all of that is before you leave Future World and head off onto the World Showcase.
If I only had one day in Orlando, I would go to Islands of Adventure with a park hopper to go over to Universal Studios Florida next door. They have the "big kid" rides.
But let's narrow this down to a single question: Do you drink alcohol?
If so then I have three words for you: EPCOT, EPCOT, EPCOT.
Bomb the park early. Hit Soaring first, Mission: Space (perhaps the most underrated attraction in the industry) Sum of All Thrills (fun enough), Test Track and the flashlight tag thing at Communicore. Then break into Turtle Talk, grab a snack at The Land food court, roll through the free Coke joint (try the mouthwash flavor from Turkey) and then blast out to World Showcase.
Moosehead at Canada (while watching Off Kilter) a traditional stout at the Rose & Crown, Grey Goose Slushie in France, good ol' Bud in the American Adventure ('cause I don't like sake), that purple wine my girl likes in Germany and the tequila bar in Mexico.
I can PROMISE you will have a great time. And you have to accept that promise because if you follow my agenda the next morning you will have no recollection of what you did the day before.
Regardless of the fact that I do not prescribe to the part of TH's touring plan that involves drinking all that Schlitz Malt Liquor, his strategy is a sound one indeed. And even without the booze, Epcot is a wonderful park, the finest this country has to offer.
However, if you do go the booze route, do try to stay conscious long enough to enjoy Illuminations at the end of the night.
As much as they say Epcot isn't for kids, it's the park that I have the most memories of growing up. When someone says "Disney World" I think of Spaceship Earth and Horizons. Apparently my first trip there was right after it opened (I was...one), and we hit all the parks equally when we would take our family trips. Of course, I haven't been since 1996, so I haven't been to AK at all or seen the new stuff at Epcot (and now Horizons is gone).....so I guess I can't TRULY be the judge.
Based on last time I was there, I would rather skip MGM (errr, Hollywood) than Epcot for sure.
Looking forward to our two week honeymoon at Disney in September. We will DEFINITELY see everything that all parks have to offer this time.
Walt Disney World
Tokyo Disney Resort