As I understand, they are both very close in terms of meaning.
E.g.
私は歌を歌えないわけではないが、人前で歌うのは恥ずかしい。
私は歌を歌えないことはないが、人前で歌うのは恥ずかしい。
Both sentences would mean: "It's not that I cannot sing, it's just that I get embarrassed in front of others."
I'm pretty sure there is a slight difference in nuance, that I can't quite grasp yet.
Is it a matter of opposing the belief of someone that you can't? (while the other is plainly a statement?)