'Able to' has a broader meaning than 'capable of'. 'Capable of' refers only to the extent of someone's personal abilities - physical, mental, intellectual, psychological, and so on. 'Able to' has the same meaning, but can also include all sorts of external factors. For example, if you say that John isn't capable of taking part in a long mountain trek, this means that he is are not physically fit enough. But if you say that he isn't able to take part, this might mean that he isn't free or is too busy at work.

In this context the words have a slight difference in meaning. 'Capable' means you have the ability to do something, whereas ' be able to' is used when stating that you are only capable of doing something under certain circumstances, for example: 'My teacher said that I would be able to go to university, if I get good marks in the exam'. / "My teacher says I am capable of going to a good university, as I already have the grades".