Graf Zeppelin was 770 ft long, carried 40 crew and 20 passengers. (Note that an American football field is 300 ft from goal line to goal line.) Boeing 747-400 is 230 ft long, carries somewhere between 400 and 600 passengers.
That means that the ground facilities to handle the zeppelin are going to be a lot bigger and you're going to need a lot more of them, to handle the zeppelins.
You'd need 20 to 30 Graf Zeppelins to carry one 747 passenger load. Fly to Tokyo Narita, or Bangkok Suvarnabhumi, and look at the 747s and 777 lined up side-by-side, and think about how many zeppelins you'd need to replace them.
A Boeing 777, flying at speeds north of 500 mph, takes about 12 hours to cross the Pacific. A zeppelin at 80 mph, or 1/6 the speed, is going to take about three days to make that trip. This means that instead of carrying one full meal, a light meal, and a snack, for each passenger, it must carry about nine full meals for each passenger, and a lot more drinking water. This also has implications for crew staffing. You're going to need a lot more pilots and flight attendants, since you're going to be running three shifts for three days. The holding tanks for the lavatories are going to have to be appropriately sized, as well: the people under the flight path do not appreciate you dumping your holding tanks on their back yard barbecues.