Would you do a dividend recap or pay down debt with excess FCF?

It all depends on your goal. If you're trying to maximize IRR, you are correct in theory; you will always try to maximize your cash distributions ASAP whenever cost of debt financing is cheaper than your equity return and your debt covenants allow you to do so. If you're speaking in terms of a typical LBO test, many LBO tests simplify to assume cash used for 100% debt paydown to keep it clean and simple.

In reality, many debt securities prohibit or restrict some / all forms of cash distribution to equityholders before they are paid out (i.e., you would want to dividend out cash, but there are minimum cash sweeps for 1st Lien, maybe restrictions on cash leakage on 2nd Lien / Mezz, etc.). Also there are obviously ongoing needs for capex, NWC and other regular business matters, so most people don't 'wind' the cash flow so tightly in a model and leave some small amount of cash building on the B/S. Obviously highly dependent on the business and financial profile, but generally the IRR doesn't change that materially in a 5+ year horizon (usually less than 5% assuming debt paydown vs. equity dividend), and the MOIC should not change materially either (i.e., cash used to pay down debt vs. dividend out is roughly the same amount of cash quantum still received by the same equityholder, its just change in timing)