As long as the values of Gibbs free energies or enthalpies of formation you are using all correspond to the same temperature and pressure conditions, there should be no difference between methods. Of course, if averaging has been used to tabulate some values of Gibbs free energy, analogous to the case of mean bond enthalpies, then there could be a difference in accuracy between methods.
You should realize that when plugging in values to the expression
, in order to be strictly accurate, you should be using values for enthalpy and Gibbs free energy that correspond to the temperature in the expression. When we calculate a temperature at which a reaction becomes spontaneous, we are assuming a little bit of error. As long as the temperature at which the values of enthalpy and Gibbs free energy plugged into the preceding equation are not extremely far from the temperature at which the reaction becomes spontaneous, then that error will be low.