Answer
2-iodo-2-methylbutane will react faster by the $S_N1$ mechanism.
Work Step by Step
We know that the structure which forms a more stable carbocation will react faster by the $S_N1$ mechanism. In the given pair,2-iodo-2-methylbutane has a better leaving group $I$, and will form a more stable carbocation. So, 2-iodo-2-methylbutane will react faster by the $S_N1$ mechanism.