There are many changes that would accelerate this reaction. Continuing with the steric effects theme, replacing the primary carbon with a methyl carbon would make the reaction even faster. To determine which reaction is faster, we need to know the mechanism. As usual, start with the S N 2 analysis. The S N 2 requirements are met, so the reaction most likely proceeds via the S N 2 mechanism.
Iodide ion is more nucleophilic than chloride ion because iodide ion is more polarizable.
Although iodide is also less electronegative than chloride, polarizability has a greater influence than electronegativity. It is hard to improve on the nucleophilicity of iodide ion, but we do know that in aprotic solvents, nucleophilicity improves with higher dielectric constant. This leaves S N 1 as a possibility, but we need to verify that the reactions could occur by the S N 1 mechanism. So the reaction can indeed occur with the S N 1 mechanism. A carbocation that is tertiary and has resonance is significantly more stable than a secondary carbocation that lacks resonance.