I have also studied the various slim digital pianos and their action relatively intensively. What is "the best"? Well, the unsurprising answer up front is: "It depends!"
All these inexpensive digital pianos have their specific advantages and disadvantages. Ultimately, you have to find out for yourself what suits you best. What became clear to me during my search: You can play and learn piano well to very well with all well-known digital pianos. As proof, you will always find enough very talented pianists who enjoy playing with the keyboard in question and qualify it as good. So you can't really go wrong with any of them. But you should find out for yourself what is most important to you personally.
The PHA4 from Roland is fascinating when you see it and play it. It somehow feels very much like a piano. It requires slightly more finger strength than the Casios. Some people like that. Others don't. The former like the resistance and the "escapment" and say that they can play very expressively with it. The latter say that it tires them too much, that they have the feeling that the keyboard slows them down a bit (feeling like wading through water). I can understand both attitudes myself. But as a beginner, you certainly can't go wrong with an FP30x or FP10. Many beginners and music students use these devices successfully. And they are also often recommended by teachers if you want something light, cheap and piano-like. And a killer feature of the FP30X is the ability to use the sound of Pianoteq elegantly via one and the same USB cable with a connected iPad, as it can be used as an audio device.
But the Casios also have a lot to offer. They are much slimmer and very light. This means that if looks, space and weight are very important, they are the right choice. The keyboards are somewhat lighter weighted than the PHA4. Somehow, however, they are also simpler. But still pleasant to play. I myself have the impression that they tire me less. I played on a Casio PX-S1000 for 3 years and have now switched to the PX-S5000. And I have to say that I got on well with the PX-S1000, but I love the PX-S5000 with the new keyboard even more. It feels better balanced and smoother. All in all, it's very high quality. But the devices with the new keyboard are significantly more expensive, so there are other options if it doesn't have to be light and slim.
Unfortunately, in the end I'm back where I was at the beginning: go to the store and try out both brands and then decide. Both are definitely suitable for a child. Because 99% of the time, the challenges lie elsewhere than with the chosen keyboard ;-)