Suppose we are driving a turbine. Does having an increase in the density of gas present an advantage over having a higher pressure delta by dumping to ambient

Suppose we are driving a turbine. Does having an increase in the density of gas present an advantage over having a higher pressure delta by dumping to ambient for a given volume of compressed-gas storage? Why would I want one tank at "high" pressure, and another tank at "higher" pressure, when I could just have one tank of "higher" pressure to begin with? Or, better: Two tanks of "higher" pressure in even less space than one of "high" and one of "higher" pressure? (If the answer is "Because turbines work better with higher densities," then: Do they work more-betterer-enough to make up for the size and complexity?)