Accuracy of the different levels of electronic structure theory is frequently studied for stationary-point properties; however, little is known about the effects of the electronic structure methods and basis sets on the dynamics of chemical reactions. Here we report such an investigation for the F + CHI S2 and proton-transfer reactions by developing 20 different analytical potential energy surfaces (PESs) obtained at the HF/DZ, HF/TZ, HF-D3(BJ)/DZ, HF-D3(BJ)/TZ, MP2/DZ, MP2/TZ, MP2-F12/DZ, MP2-F12/TZ, CCSD/DZ, CCSD-F12b/DZ, CCSD(T)/DZ, CCSD(T)-F12b/DZ, OQVCCD(T)/DZ, B97-1/TZ, PBE0/TZ, PBE0-D3(BJ)/TZ, M06-2X/TZ, M06-2X-D3(0)/TZ, B2PLYP/TZ, and B2PLYP-D3(BJ)/TZ levels of theory, where DZ and TZ denote the aug-cc-pVDZ and aug-cc-pVTZ basis sets with a relativistic effective core potential and the corresponding bases for iodine. Millions of quasiclassical trajectories on these PESs reveal that (a) in the case of standard methods, increasing the basis from DZ to TZ decreases the S2 cross sections by 20-30%; (b) the explicitly correlated F12 reactivity is converged with a DZ basis;