It is difficult to recommend one resort over the other without knowing more about the situation. Which is the better choice depends upon many factors. The blanket answer is yes, AKL is worth the price difference. It is a deluxe hotel and the CSR is a moderate. In WDW you very much get what you pay for.
My opinion:
If the budget allows, I would stay at AKL. I prefer the deluxe resorts over the moderates
However, I am usually fine without doing 'extras'. For example, I have found the
MVMCP to be a huge disappointment. (Just my opinion, of course, others will disagree I am sure. It seems like paying a premium for a few extra hours in the MK.)
We spend a lot of time enjoying the resort and its facilities. Also, it is important to me to have a balcony to relax on with a coffee or a drink before bed.
However, I have stayed at the moderates as well as the values many times and enjoyed the trips tremendously. It all comes down to budget, how you plan to spend your vacation and who you are travelling with. We tended to do more value and moderate trips when the kids were young. Now we are older and slower so we never try to see a rope drop and are satisfied with much fewer hours a day in the theme parks. I have spent days in Epcot without getting on a single ride. My priorities are quite possibly very different from yours.
You have to decide on what you want. Do you want a more luxurious resort with slightly larger rooms, a balcony, and interior hallways or do you want to spend the $$$ on a late night party in the MK or perhaps a special tour? Will you even be at the resort enough to enjoy the slight differences? CSR does offer a lot for a moderate resort. There is a spa/salon and a fitness centre. There is the option to book a business class room. Dining options are great at CSR. (But better at the AKL) The pool is awesome at both resorts. The rooms are 314 sq ft compared to the 344 sq ft at the AKL, I believe. Not a huge difference. There are beautiful grounds to walk around at CSR. The animal viewing areas are great at AKL, but we liked walking around CSR more.
Both are great resorts. I am sure that you will enjoy whichever you choose.
Good luck!