For example, is there an output efficiency difference between using a 400nm pump beam or a 500nm pump beam through a BBO nonlinear crystal, assuming that they both are phase-matched?
The spontaneous parametric down conversion (SPDC) is second order non-linear effect. Its efficiency does not depend upon the pump wavelngth.
But it depends upon the non-linearity of the medium in particular the specific term of the effective non-linear coefficient term (of BBO crystal) involed in the phase-matching.