Summary: In plasma physics, linear instability calculations can be implemented either as initial value calculations or as eigenvalue calculations. Here, comparisons between comprehensive linear gyrokinetic calculations employing the ballooning formalism for high-\(n\) (toroidal mode number) toroidal instabilities are described. One code implements an initial value calculation on a grid using a Lorentz collision operator and the other implements an eigenvalue calculation with basis functions using a Krook collision operator. An electrostatic test case with artificial parameters for the toroidal drift mode destabilized by the combined effects of trapped particles and an ion temperature gradient has been carefully analyzed both in the collisionless limit and with varying collisionality. Good agreement is found. Results from applied studies using parameters from the Tokamak Fusion Test Reactor (TFTR) experiment are also compared.