Is isobutyl chloride or ethyl chloride more reactive in an SN1 reaction?
The inductive effect of the methyl groups should help stabilize the carbocation formed from 1.
The answer may be a bit clearer if you add equilibrium to your thinking. 


The initial dissociation of the 1 to form carbocation A is the rate determining step.  However the rearrangement of A to B should be relatively quick, and will drive the initial dissociation forward by Le Châtelier's Principle.  

In contrast, 2 has less stabilization by the inductive effect, and there is no possibility of a rearrangement.