Modern Buddhism, including Zen, assures us that there is a payoff to being aware of the moment, which I need add, is only the truth of sense certainty. That's not much. What it does not say, there is no certainty as to where all this awareness is taking us. In the context of traditional Buddhism, there is very little said, if at all, about being aware of the moment. Nevertheless, awareness of the moment has become what can only be described as pseudo-enlightenment. This is all the typical Westerner, it seems, can relate to. Nirvana is out of the picture. For the average person it sounds like mumbo-jumbo that comes with such baggage as nirvana is deathless and eternal; nirvana is realized in the very self and so on.
Back to the question. Where are we going with being aware of the here and the now—this very moment? For example, what is the payoff to practicing awareness at my crappy job, being aware of every crappy moment of looking at a computer monitor doing shit I hate just to pay for a roof over my family's head, not to mention paying the doctor's bill for my kid's recent ear infection?
Awareness of the moment can help to mollify the inner tension and frustration we often feel at the end of the day—that's about all. We live in a culture with a Darwinian mind-set where the fittest human animals are trained to prey on the weaker so that life, essentially, is hell despite the fact that animals and humans can be caring, giving and loving were they not always put between a rock and a hard place by the ideologists and their followers who believe in the model of natural selection and survival of the fittest.
I went through the 1960s optimistic that awakening was achievable. As I can remember, there wasn't any of this awareness of the moment practice yet as if this was enlightenment. If there was, it was in the beginning stages. Aiming for nirvana or kensho (both are the same) is the better course. Being aware and vigilant; paying attention to details and taking care of the little stuff so you don't have to worry about the big stuff are all important. Still, nirvana has to be the goal. It has the real payoff. Sincere interest in achieving nirvana—not just lip service—helps to ennoble us since it makes us open up more and dig deeper into our being. Nor are we wont to buy into our crap predatory culture. This is the start of renunciation.