Hi, I am new to disboards, but I have really enjoyed reading the threads. Very informative!!
First of all,
I need some advice please. ... My children are boys, ages 10 and 11. Based on their enjoyment, which park should we do twice?
Since your boys are 10 and 11, they might actually find Epcot more to their liking for a second visit. It will, of course, depend on how "worldly" they are -- whether or not they're interested in international affairs and the like.
I'm afraid they'll find most of the rides in MK kind of tame (excepting the mountains), and AK is at best a half-day park (but by skipping it, your boys will be missing two world-class rides -- Dinosaur and Expedition Everest). DHS has several headliners (Toy Story Midway Mania, Tower of Terror, Rock-n-Roller Coaster, Star Tours), but once you're done with them, there's probably not much they'd want to repeat.
But for me (and this is subjective), I could spend two whole days in Epcot -- the attractions I most consider "re-visitable" include Mission:Space, Test Track (disclaimer -- I haven't been on since the refurb), The Land and Seas pavilions, Mexico, Japan, Germany, France and Norway. Plus, I just like the feel of the place.
However, most people will wait until they get there, and let the group decide which park they'd like to revisit based on how well their first day went.
My opinion, worth what you paid for it. No matter how you decide, you'll enjoy your trip and have a great time!