The methods are quite different, but I think at root, it's just more being able to take advantage of much more training data.
The 97.53% "human performance" number comes from my paper from a few years ago [0]. We initially thought that there's no way we would be able to do that well on this task (manually) either, but then we tried it and our scores were much higher (very close to 100%). So the verification task on LFW is actually not that hard, although in part it's because the dataset consists of public figures and therefore you can recognize many of the people outright if you've seen them before. (We tried to measure this in our human studies but found it to be inconclusive.)
3% is not the right way to look at error rates, btw. See [1] for why. But also, face verification is more of a low-level building block for recognition, because most real-world applications don't directly care about saying whether two faces are the same person or not ("verification"), but "who is this person?" ("recognition"). A simple way to build recognition from verification is to compare a test face against all faces in the database, and then take the one that gets ranked highest. In that (simplistic) scenario, your recognition rate scales (very roughly) as acc^lg(N), where N is the number of people in your database and acc is the verification accuracy. So if, e.g., you had 100,000 people to recognize from and your verification accuracy was 97.53%, you might have a recognition accuracy of ~66% (very roughly!), which is not great.
Finally, there are already lots of applications to face recognition other than surveillance, and many more waiting to be discovered.
[0] http://homes.cs.washington.edu/~neeraj/projects/faceverifica...