Let's stop arguing which is closer to where. I have done a map for us.
I have placed circles around the two sites in question as well as all other local pools. The circles are not an exact size but I would suggest about 2/3rd miles radius.

What is striking about this map is that whilst there is some overlap from the Dartmouth Road site with both Crystal Palace and The Bridge, this overlap is much more pronounced for Willow Way. In about 1/3 of the circle of Willow Way people are closer to another pool.

Now look to the north of the circles, you can see how far it is for many people in SE23 to travel to there nearest pool. For most Willow Way will still be closer than East Dulwich and Ladywell (on its current site), which are represented by the edges of equal sized circles at the top. But the argument that Wells Park Estate need a pool 5 minutes away when they have two 10 minutes away does not do justice to the residents of Honor Oak Park and Perry Vale ward who will not even have one 15 minutes from their house.

You have to ask the question how long you expect these three pools to continue to survive and I believe Max has a good point when he says that if option 3 does get the go ahead in 20 years time one of the two Sydenham Pools will be shut down.

I hope this map is useful, feel free to interpret it differently if you wish.