Feint is awesome when you're solo.
Red Lotus can't miss too, but it costs MP, twice as much TP, and does less damage than Feint.
Optimal time for using Feint is after multi hit abilities. Multishot, Barrage, Flurry, etc sometimes don't get all their hits in, so it's nice to follow it up for extra damage using Feint.

But if you're in a party or raid, then Feint's usefulness is diminished.