Which do you think is the best method?
As with most machine learning, each approach has its strengths and weaknesses, and other than a little bit of intuition:
Policy-based methods are strong in large or continuous action spaces, and/or where there is a simple relationship between state and optimal action. E.g. controlling a robotic arm with continuous action space.
Value-based methods are strong where there is a simple relationship between state and value under an optimal policy. E.g. in a maze game.
It may not always be clear which is best, in which case experimentation is required. If using neural networks, there will then be a large number of hyper-parameters on each approach, so it may be hard to come to a strict conclusion about which is better. Although you can include "easy to find a working model" or "robust for a range of hyper-parameter values" as benefits of any type of model if you wish - these are important practical benefits of any approach, developers rarely want to do 100s of experiments to tune a learning rate parameter for example.
Which is the best way to do AI? Or some combination of the two?
Actor-Critic, as seen in Asynchronous Advantage Actor Critic. A3C and A2C (deterministic variant of A3C) is producing current state-of-the-art results in video games. This is a combination of both approaches, where the agent maintains two related models - one, the Actor, generates a policy directly by looking at the state, and the second, the Critic, tracks the estimated value of each state. Often, these two models share some parameters - e.g. using neural networks, the initial layers may be the same for both.