At low to mid RPMs, the 5.3 Hemi and the 3.0 EcoDiesel are pretty evenly matched.
3.0 EcoDiesel Peak Horespower = 240 HP @ 3,600 RPM
5.7 Hemi Peak Horsepower = 395 HP @ 5,600 RPM
3.0 EcoDiesel Peak Tporque = 420 lb/ft @ 2,000 RPM
5.7 Hemi Peak Torque = 410 lb/ft @ 3,950 RPM
3.0 EcoDiesel Redline = 4,800 RPM (upshift @ 4000 RPM Wide Open Throttle)
5.7 Hemi Redline = 5,800 RPM
This isn't a low revving diesel like the ones you'll find in commercial trucks or in a diesel pusher.
Looking at the numbers, both engines have about equal torque, but the 5.7 Hemi has to turn twice as fast to achieve it. Since Horsepower = Torque x RPM x 5252, the Hemi makes twice as much horsepower at it's torque peak as the EcoDiesel.
Looking at the torque vs. horsepower charts, the two engines have about the same amount of pulling power up to their midrange RPMs. The 5.7 Hemi develops the same amount of pulling power at 2500 RPM (43% of it's 5,800 RPM redline) as the 3.0 EcoDiesel does at it's 2000 RPM torque peak (42% of it's 4800 RPM redline). Above these speeds the 5.7 Hemi is the clear leader with it's torque continuing to increase up to 3,950 RPM while the EcoDiesel's torque falls off above 2,000 RPM.
In other words, below 2,000 RPM for the EcoDiesel or 2,500 RPM for the Hemi, the two engines will pull about the same. Above that point the EcoDiesel's power will tend to level out while the Hemi continues increasing torque up to 3,950 RPM.
Since it takes more fuel to create more power, or less fuel to create less power, I suspect the Hemi will closely match the EcoDiesel's mileage unless you ask the Hemi for more power. If you do, the Hemi's MPGs will go down accordingly.
Diesel fuel does have an inherent MPG advantage over gasoline due to it's greater BTU energy per gallon. But diesel now costs more per gallon than unleaded gas, which may negate part of it's cost advantage.