It's a toss up which is the best way to squeeze maximum miles per buck out of chains and cassettes. Many old timers ride chains and cassettes together until they just won't run any more. Typically this is somewhere between 2% and 3% stretch, after which both have to be replaced, since the cassette is too shot to run with a new chain. One drawback of this method is it can be hard on chainrings and you might find yourself replacing everything.

Most people today replace chains nearer 1/2% stretch to save the cassette so it'll run with a new chain. Usually you can run 3-5 chains on a cassette this way, and run the last chain beyond 1/2% stretch since the cassette is shot anyway.

Which is smarter depends on the relative cost of chains and cassettes, but as hillrider points out using 4 chains to get the same life as one barely makes sense unless the cassette does outlast 4 chains, and the savings on chainrings offsets the added chain cost.

There's a third way, which many find to yield the most miles per drivetrain dollar. That's to rotate 2-4 chains at regular intervals, running the entire package until it dies. I manage my bikes this way, and can get 15-25,000 miles out of the package, and sometimes more.
There's no one answer for everyone, and variables like what percentage of the total mileage is on only a few sprockets, can alter the economics. But just like chain lube, everybody figures his way is the smartest.