Actually, the literature so far suggests that convolutional networks have better accuracy than capsule networks on many tasks, so it's by no means clear that capsule networks are superior across the board to CNNs. This is perhaps not surprising; we have many years of experience working out how to engineer convolutional networks so we get the best possible performance out of them, whereas capsule networks are still new and haven't yet benefitted from that degree of engineering. So, we might see further improvements in the performance of capsule networks in the coming years, now that they are getting more attention.
There are some specific areas where capsule networks have significantly outperformed convolutional networks. Those seem to be primarily those where viewpoint invariance is especially critical. There are others where so far they are worse. For instance, capsule networks so far have done significantly worse than convolutional networks on CIFAR10. There is active research and an active debate in the machine learning community about how well capsule networks will perform. I think it's too early to say how that will pan out.
As far as amount of training data, it is likely that this will depend on the task as well, and is probably an open problem at this point. I would imagine that capsule networks might need significantly less training data for tasks where viewpoint invariance is especially central, but that might not be true across all tasks.
In general, not a lot is known yet about the performance of capsule networks, and the answer to most questions of the form "how well will capsule networks perform on X?" is "you'll have to try it and see".