We've stayed at both WL and AKL several times each. Lots of "it depends" in my answer regarding the pools!
AKL pro: The fact that, as BuzzyBelle mentioned, you have access to two feature pools at AKL - both the main AKL pool and Kidani. The variety is great. At one point, when pools were more of a focus for us, we identified AKL pools as second to only SAB at BC/YC. Huge water playground area at Kidani and fun waterslides at both.
AKL con: There is no "quiet pool." So if you don't like mid-afternoon pool games (like our 18yo) you are out of luck! There are pool games at both pools in the afternoon and there is nothing quiet about them. Also, we always think we're going over to the Kidani pool during our stay, but we only make it over there either once or never per stay. It's really not that far (maybe 5-10 minutes) it's just that once everyone is changed into swimsuits, it just seems easier to stay at Jambo to swim. Also, there are a number of areas in Kidani and the cool theming obscures the stairs to the slide, so it's not as easy to have eyes on the kids all the time. The main AKL pool is kind of split up now that the fences are up, too.
WL pro: New villas pool! It looks fabulous. No water slide, but I'll sacrifice the slide for the lack of loudspeaker-fueled pool games. Also, plenty of food and drink nearby at Geyser Point. The whole area is just so fresh and clean. The water play area at the main WL pool is fantastic for little kids. While our youngest has enjoyed the Kidani splash area (and it's very large) he prefers the contained water playground at WL. We also find it far easier to supervise the kids at the WL pool - there seem to be fewer areas to swim/run into, so we could easily follow them when they were zipping away. When they became strong swimmers, we could actually sit down in one spot for a bit! Also, the villas pool is right next to the main pool, so we have access to two pools that we're likely to actually use.
WL con: The main pool gets very crowded sometimes, and the pool game noise can really permeate the area. Also, the slide is super tiny and wasn't very interesting to our kids past age 7ish.
We prefer WL pool right now, but we've changed our minds over time and just may change them back again. Both are great choices!