The integral expressions of classical S matrix theory are tested against quantum mechanical results and classical path-forced quantum oscillator results for vibrational transition probabilities in collinear collisions of atoms with harmonic and Morse vibrators for the H+Br2 and He+HBr mass combinations. The interaction potential is assumed to be a repulsive exponential function. The energy range studied (in units of ℏ) is 2-10 for H+Br2 and 2-6 for He+HBr. The integral expressions are found to be accurate within a factor of two for almost all transition probabilities greater than 7×10-3 but to be very inaccurate for very small transition probabilities. Quasiclassical trajectory histogram methods are found to be accurate within a factor of two only for transition probabilities greater than 0.15. Neither the integral expressions of classical S matrix theory nor the quasiclassical trajectory histogram method are found to be as generally accurate as the classical path-forced quantum oscillator results.