That's a bit of a trick question, because the answer I give is: neither. What one wants to do is apply the optimum amount of water to the turf, and that can be done by light and frequent irrigation, or it can be done by deep and infrequent irrigation. This chart illustrates how soil moisture may change over the course of a month when two different irrigation regimes are used.
The optimum amount of water varies, with grass type, season, soil, type of surface one tries to produce, weather, type of irrigation system - these and other variables form an extensive list. But one thing that is consistent is that at any one time, for any one location, there will be an optimum amount of water, and achieving that, I suggest, should be the main focus, rather than focusing on how frequently water is applied.
At the Asian Turfgrass Center, we followed this approach in the maintenance of more than 50 varieties of grass. I probably would have tried to apply a lot of water, to fill the soil to field capacity, and then allowed the grass to use much of that water, before irrigating again - this is the deep and infrequent approach - but we had a small irrigation pump and it was easier for us to apply just enough water to meet the grass requirements.
In a discussion with Dr. Doug Soldat from the University of Wisconsin, he explained clearly that one could actually maintain a drier soil, one that can supply just the amount of water the grass will use, while still maximizing the amount of air in the soil, not with infrequent irrigation, but rather with frequent application of just the right amount of water. Since then, I have focused more on ensuring the right amount of water is available to the grass, rather than what the frequency of irrigation is.
And in so doing, I have often been surprised at what a fine surface is produced, and in many cases a verdant one, even in soils that are maintained at a low volumetric water content (VWC).