For me the answer is a no brainer. Go to the AKL!!!! But let me give you the long answer as to why. This is probably more of an answer than you bargained for, but you did ask to be convinced.
Granted, there are some people who really like the value resorts. While I've never been one of them, I'll admit that AoA does has some appeal if the family suite (without paying a fortune) is something you are attracted to. Having two bathrooms and a seperate bedroom for mom and dad is a big plus. While not our cup of tea, food court dining can be appealing to those who aren't interested in the time or expense of sit down meals, or more adventurous flavors. If having some privacy and the extra bathroom, along with the speed and convenience of food court dining, is important to you then an AoA suite may be the way to go.
However, if privacy, an extra bathroom and a food court aren't necessary, I think the AKL has more to offer in the way of what I call a real Disney experience. What do I mean by real, you ask? Well, real in the sense of what I believe Walt Disney intended Disney resorts to be. An immersive experience, just like Walt envisioned The Polynesian Resort to be when he drew up The Florida Project. Ultimately, for me it comes down to the difference between theming and decoration.
Let me elaborate on what I see as the differences. Just like Walt's Polynesian Resort was intended to instantly transport you from the central Florida swamp to Polynesia itself, from the traditional Polynesian style long houses right down to the burning tiki torches........the AKL takes you off to Africa, immersing you in the theme, from the traditional African lodge design right down to the decor and the surrounding savannahs. It's the type of immersive experience I think you are assured at Disney's deluxe resorts, where the intended theme is largely carried throughout the entire resort. I don't believe the moderate resorts (outside of what I like to still call Dixie Landings) accomplish that, and I certainly don't think the value resorts do.
Now let's look at AoA. It's description purports to let you become a part of your favorite Disney animated film. But how do they accomolish that? Well, from what I've seen, I don't think they do. Why? Because the resort relies on decoration as opposed to theming. What does that mean exactly? Well, if I want to become a part of the animated movie Cars, I want to BE in Radiator Springs. I want to walk through the town on my way to my room, and feel like I'm in the film.....as opposed to just walking past a big Mater decoration thrown in a courtyard. The rooms are the same way. Don't give me a Cars suite that is nothing but a bunch of decoration thrown throughout the room...give me a Mack suite that is themed such that I feel like I AM Lightning McQueen inside Mack on my way to the final Piston Cup race.
Well, enough about this somewhat abstract difference between theming and decoration, let me talk about actually staying in the resort, as we spent a night at the AKL just a few weeks ago. While I haven't stayed at AoA, I have stayed at other value resorts, and AoA looks similar. For us the resort experience was ok, but missing something. The rooms, the furniture, the amenities were ok, but lacked some of what my family wants in a resort room. I want real wood furniture, and a closet, and a plush bed.....things the value resorts don't really provide. Go ahead, call me a deluxe resort snob....but if you can get the deluxe resort experience I think you should take it. As for the AKL itself, the theming may not be everyone's cup of tea, but if it appeals to you it is well done. The lobby is expansive and beautiful. The rooms (while not a suite) are good sized, well appointed, and very comfortable. However, the real appeal of the AKL is in the surrounding savannahs, and all the places you can explore throughout the resort, including the two well themed main pools. I doubt there will be much to inspire one to just explore the AoA resort, at least not for very long, but at AKL you can spend hours just poking around, stopping at lookout points to survey the animals on the savannah's. As you walk down any hall, regardless of whether or not you have a savannah view room, you will be compelled to stop at the large windows to see what animals are out on the savannah. Grab a drink, sit near a fire pit while the cast members posted at the lookouts tell you about the animals, don some night vision goggles to see the animals in the dark. That type of stuff is what sets the AKL experience apart. I will say, the restaurants weren't my wife's cup of tea, as she is not an adventurous eater, and some of the african and indian flavors didn't appeal to her, so research the food options and make sure thye will be to your liking. Location wise, if you have to jump on a bus at either AoA or AKL to get to a park, I doubt it will take significantly longer to get to any park from one resort versus the other.
Hope I've given you a few things to think about.....let me know if I convinced you!
I looked at what else we could do for the same money and discovered its only $30 more to get a regular room at AKL. Not a savannah view and not a bunkbed room. 
