A detailed systems analysis code has been used to compare the projected cost of electricity (COE) for inertial fusion energy for direct drive (DD) and indirect drive (ID) target scenarios, based on a diodepumped solid state laser driver with Yb:S-FAP (Yb doped Sr5(PO4)3F) gain media.Previously published target gain curves which resulted in a target gain at the optimal DD operating point that is 30% higher than that for the ID scenario have been used. This gain advantage for DD is offset by a requirement for improved beam smoothing, which was obtained via smoothing by spectral dispersion (SSD) with a 1 THz bandwidth at 349 nm. Such a large SSD bandwidth has a number of effects on laser performance, including greater risk of optics damage from non-linear effects, lowered harmonic conversion efficiency, altered extraction parameters and higher front-end costs. The non-linear effects, which contribute to optical component damage by amplification of intensity non-uniformities, were parameterized through a constraint on the maximum allowable B integral (i.e. the total average phase retardation due to the non-linear indices of all materials traversed by the beam). If we constrain B to be no larger than 1.8 rad, which is the presently accepted safe value based on observations in single shot glass laser facilities, the COEs for DD and ID are predicted to be the same within the uncertainties. If technology permits the B limit to be raised, the optimized COE for DD is predicted to decrease relative to that for ID.