The Arduino board-level design is not aimed at being a low-power thing. It has a relatively inefficient regulator, and extra chips that consume current and aren't chosen to be low-power, either.
The Launchpad, since it showcases a chip specifically aimed at low power consumption, does somewhat better at the board level (but also has different behavior, WRT things like max input voltage, etc.)
Chipwise (atmega328p vs MSP430Gxxxx), it's harder to pick a winner. Both are capable of numerous and relatively complex power-saving modes, and the overall consumption of a design tends to depend more on how well you manage to use those, than any particular number specific to the chip itself. It does look like the msp430 chip will have a lower power consumption when "on" at 16MHz (according to spec sheets. About 5mA vs 8mA?)