I've hunted both and I'd take Africa any day.
First off, in many areas you can hunt Africa cheaper than a fully guided trip to AK. Some of the package hunts in South Africa or Namibia can be done for less than $5K for 5 or 6 species with extras species added on for the cost of trophy fees. Compare that to a guided moose and caribou hunt in AK. Even if you want to hunt on your own, AK is expensive and you can do unguided hunts in both Zimbabwe and Cameroon if you don't want to use a PH.
Second, there are a lot more species to hunt. AK game is actually pretty limited when you get down to it. There are less than a dozen huntable species and you can legally hunt over 200 different species in Africa.
Third, the safari industry is well established and the representatives in the states take care of everything including airfare, visas, firearms permits, trophy shipping, customs clearance etc... It is a very simple process and is handled without extra fees or hassles.
Fourth the people in Africa are great and it is good to be exposed to different cultures.