In the figurative senses, a point of view and a viewpoint are essentially the same thing. They both refer to an attitude or a way of thinking about a particular subject, e.g.
Try looking at things from a different viewpoint.
That being said, it is a fact that “point of view” is much more common than “viewpoint”. Take a look at the following diagram, showing the relative frequencies of the two phrases in English literature:
So, if you want to stick to one of them, “point of view” would be a better choice, since it will be more universally accepted.
The word “viewpoint” can also be used in the literal sense as a “point from which something is viewed”, and it is essentially synonymous with the word “angle”, as in