I've stayed at both, and IMHO I liked the WL, but LOVED AKL.
There is a difference, despite the fact the look is similar as they were designed by the same man.
WL - Think Pacific Northwest. Tall pine tree's, gives off a real "staying in the mountains, winter-type feel" to it. It seems when I go there, it is the smell (good smell!) that gets me. It reminds me of a campfire, that homey-lodge type feel. Dark browns, forest greens, beige colors. Gysers, walking in the forest, etc. Again, think Oregon, Washington State, USA
AKL - Think Kenya - Africa. Much more exotic, more international. Many of the CMs are from various African countries. Animals all about. African story telling, animal watching. More colorful. Unique decore in lobby area. Think Kenyan Animal Reserve lodge. Restaurants serve food with an African flair. (Jiko is excellent) Pool is very large, zero entry, modeled after a African water hole (you will notice the color is a bit different - beige/greenish). You really get the feel that you could be in Africa!
Therefore, it really comes down to personal likes. I tend towards the more exotic, things I cannot experience in North America, therefore this is why I liked AKL so much. However, others like the feel of WL for their own personal reasons.
Both hotels are deluxe properties, so size of rooms, style (with exception of color schemes, etc), amenities are very similar.
I hope you understand my descriptions....... and I hope this helps you decide. Either way, you'll love your stay!
