Sadly for the Razr M, it's a Verizon exclusive, where the other two devices are available on all major U.S. carriers. Given the fact that all three of the smartphones being considered here are 4G/LTE capable, the Razr M's confinement to Verizon -- which does not offer unlimited data plans -- is unfortunate.
Advantage: iPhone 5/GS III Mini
VALUE/FINAL THOUGHTS
In some ways, it's a little misleading to directly compare the iPhone 5 -- a true flagship phone, aimed at high-end consumers -- to the Galaxy S III Mini and the Droid Razr M, which are mid-market devices.
However, while the iPhone 5 is probably the best smartphone in this size class -- it's tough to argue with that display and graphical prowess -- it says a lot that the Razr M is at least close behind, while selling for half as much money. (Samsung hasn't released pricing information for the Galaxy S III Mini at the time of this writing.)