I have both. Both are good. P90X3 is a 90 day program. 21 day fix is a well, 21 day program.
So you get more discs with P90X3. I honestly think P90X3 is the single best fitness purchase I have ever made. It's not like P90X exactly - especially if you elect to do the lean rotation. And there is great variety.
21-Day Fix has good, sound workouts and I like the instructor. She's more straight forward and if Tony drives you crazy, I would go this route.