Both are possible, but the first is slightly more natural, since reference is to a relatively specific/limited ability. Where it is to a more generalized ability, then 'capable' is more likely to be used, e.g.
He is capable of reciting entire poems from memory.
As long, however, as you make sure of using the correct grammatical construction for each (able to V, capable of Ving), you do not need to overly concern yourself with semantic differences. They will be interchangeable much of the time.