How can I answer a question like that? If I'm hungry, a carrot might be good. I don't eat sticks. On the other hand, if a dog attacks me when I'm out walking, I definitely want the stick.
Now, on a more serious note, I think the carrot, i.e., the reward or incentive, is more effective than the stick, i.e., the threat of punishment. I'm not saying that aren't circumstances where a mild threat can be effective, just that it is normally that most effective. Having raised 4 sons, I learned some of this the hard way, but by and large, I learned it well. The carrot can be many things. For example, letting a child know that you love and trust him/her is a carrot as it can result in them wanting to please you. On the other hand, severe punishment may make them resent and hide feelings from you.
I think President Obama is trying the carrot approach as much as possible in dealing with our "supposed enemies". I think his approach would be more effective if his political rivals gave him more support. There are just times when he has no choice. I won't draw that point out any more, but I do believe it is the best approach.