Both are typical Tier 3 schools and rather close in research rankings. UC-Boulder is not particularly strong for Finance placement-wise; in comparison, Pitt is clearly better: https://business.pitt.edu/phd/phd-student-job-placements/.
No, research domains are not said to become old-fashioned or obsolete; rather, they evolve. Faculty research areas at both UC-Boulder and Pitt are broad enough to cover yours, be they AP or CF substantively or textual analysis or other statistical techniques methodologically. In weighing on admissions offers, a school's placement performance shall be an overarching consideration.