Which is more reactive, chlorine radical or chloride ion?
I think we can also approach this from an energetics perspective. Reactivity can also be seen to be related to thermodynamic stability in the following manner: The more thermodynamically stable a chemical species is, the less reactive it is. With this in mind, we can look at the enthalpies of formation of $\ce {Cl.}$ and $\ce {Cl^-}$. 

Your question is slightly vague as you did not state the specified state of the substance. This can critically affect the answer. The reactivity of a heavily solvated $\ce {Cl^-}$ ion is certainly different from that of a free $\ce {Cl^-}$ ion in the gaseous phase. 

By definition, the enthalpy change of formation, $\Delta H_f$, of an element in its standard state (e.g. $\ce {Cl2 (g)}$) is $\ce {0}$. $\ce {2 Cl.}$ are produced from the homolytic cleavage of the $\ce {Cl-Cl}$ bond in $\ce {Cl2}$. Knowing the bond dissociation energy of this bond to be $\ce {+242 kJ/mol}$, we can approximate $\Delta H_f$ of $\ce {Cl.}$ to be $\ce {+121 kJ/mol}$. 

Similarly, the gaseous chloride ion can be produced from the gain of an electron by $\ce {Cl.}$. The first electron affinity, $\ce {1st E_a}$, of chlorine is the energy change when one mole of electrons is acquired by one mole of these gaseous chlorine atoms to give one mole of singly, negatively-charged gaseous $\ce {Cl-}$ ions. $\Delta H_f$ of $\ce {Cl- (g)}$ can thus be approximated as $\Delta H_f$ of $\ce {Cl.}$ + $\ce {1st E_a}$ of chlorine . Since this $\ce {1st E_a}$ is $\ce {-349 kJ/mol}$, this enthalpy change of formation for $\ce {Cl^- (g)}$ can be approximated as $\ce {-228 kJ/mol}$. 

As can be seen from energetics data, $\ce {Cl^-}$ is more stable than $\ce {Cl.}$ in the gaseous phase. Thus, we may say that the $\ce {Cl.}$ is more reactive in the gaseous phase. Furthermore, being charged, $\ce {Cl^-}$ is solvated by water molecules in aqueous solution, further increasing its stability as it has ion-dipole interactions with the neighbouring water molecules. Electrically-neutral chlorine radicals would not experience this solvation effect, thus they would also be more reactive in the aqueous phase. In non-polar solvents, $\ce {Cl^-}$ and $\ce {Cl.}$ would have similar reactivity as in the gaseous phase since they do not experience starkly different solvation effects. Overall, based on energetics, we may say that $\ce {Cl.}$ is generally more reactive than $\ce {Cl.}$. 

Additionally, it is important to point out the difference in the type of reactivity of the two different chemical species. Being negatively-charged, chloride ions participate in ionic reactions, involving charged species. These reactions include nucleophilic substitutions, as well as nucleophilic additions. On the other hand, chlorine radicals mostly participate in non-polar reactions, involving mostly radical species, such as free radical substitutions.