We compare the yields of {sup 44}Ti and {sup 56}Ni produced from post-processing the thermodynamic trajectories from three different core-collapse models-a Cassiopeia A progenitor, a double shock hypernova progenitor, and a rotating two-dimensional explosion-with the yields from exponential and power-law trajectories. The peak temperatures and densities achieved in these core-collapse models span several of the distinct nucleosynthesis regions we identify, resulting in different trends in the {sup 44}Ti and {sup 56}Ni yields for different mass elements. The {sup 44}Ti and {sup 56}Ni mass fraction profiles from the exponential and power-law profiles generally explain the tendencies of the post-processed yields, depending on which regions are traversed by the model. We find that integrated yields of {sup 44}Ti and {sup 56}Ni from the exponential and power-law trajectories are generally within a factor two or less of the post-process yields. We also analyze the influence of specific nuclear reactions on the {sup 44}Ti and {sup 56}Ni abundance evolution. Reactions that affect all yields globally are the 3{alpha}, p(e{sup -}, {nu}{sub e})n and n(e{sup +},{nu}-bar{sub e})p. The rest of the reactions are ranked according to their degree of impact on the synthesis of {sup 44}Ti. The primary ones include {sup 44}Ti({alpha}, p){sup 47}V, {sup 40}Ca({alpha}, {gamma}){sup 44}Ti, {sup 45}V(p, {gamma}){sup 46}Cr, {sup 40}Ca({alpha}, p){sup 43}Sc, {sup 17}F({alpha}, p){sup 20}Ne, {sup 21}Na({alpha}, p){sup 24}Mg, {sup 41}Sc(p, {gamma}){sup 42}Ti, {sup 43}Sc(p, {gamma}){sup 44}Ti, {sup 44}Ti(p, {gamma}){sup 45}V, and {sup 57}Ni(p, {gamma}){sup 58}Cu, along with numerous weak reactions. Our analysis suggests that not all {sup 44}Ti need to be produced in an {alpha}-rich freeze-out in core-collapse events, and that reaction rate equilibria in combination with timescale effects for the expansion profile may account for the paucity of {sup 44}Ti observed in supernova remnants.