Great questions, though it's hard to put both workout programs side by side as it's not a simple apples to apples comparison but more like apples to oranges. Both programs are capable of offering a huge physical challenge but each has it's own approach and it's own target results. I'll explain.
The P90X workout program is a 90 day system which could otherwise be considered an "at home boot camp". You will need a chin up bar, a chair, a set of dumbbells and/or bands, shoes, plus about 1 hour to 1 hour and a half 6 days a week. The 7th day is an optional stretch or complete rest day.
From first hand experience I like to look at P90X as a "all-in-one" program. It is not designed to just bulk you up, it's not going to just help you lose weight, it's not just balance, and it's not just cardio.
P90X workout program just tosses a bit of everything into the equation. You lift heavy one day (or light if you want);, you're punching and kicking with Kenpo karate another day, and to top it off on other days you will be doing 1 and a half hours of Yoga for a complete mind/ body/ soul adventure.
You will go through three phases of 1 month each in P90X with each month switching it up. Most of the cardio, stretch, and balance routines stay the same. The difference in each phase is that you change out the resistance workouts so that your muscles are constantly challenged so they will always be receptive to the workout rather than plateauing.
Shaun T Insanity takes a completely different approach. The workout program is 60-days in length and is based solely on Plyometrics, Core, and Cardio training. You will not lift weights, you will not do chin ups, you don't need a chair, and the workouts range from 35-45 minutes the first phase to 1 hour and 15 minutes the second phase.
You will need very good shoes, preferably a mat to jump on, and near perfect form to avoid injury.
Both video's can be purchased at http://www.beachbody.com/