I want to control a single DC motor with an Arduino. Why would I use an Arduino motor shield as opposed to an H-circuit and a MOSFET?
The major benefit to using a shield vs building the same circuit yourself is convenience. Assuming that your circuit is identical to the circuit on the shield then they should both work in an identical manner (barring any minor variations due to the quality of solder joints or circuit paths). The nice thing about the shield is it is almost plug and play. It has the same footprint as the Arduino and you don't have to design and assemble the circuit on a perf board. Generally, you will end up with fewer wire leads running around making for a cleaner assembly and easier prototyping.