I tried to do P90X at home by myself, and I found it really hard to stay motivated. Maybe because I'd already done it with friends, but a few other things came into play. First, the workouts are a minimum of 1 hour. The yoga routine is 90 minutes, so it is a very large daily commitment. As a Mom, it's hard for me to find that amount of time each day because I also need a few minutes to cool down (literally cool my body temperature) plus time to shower and get ready. And, I can't rely on myself to commit to that every day after the kids go to bed - there's too much other stuff to do (dishes, laundry, cleaning, relaxing) during that time. The other problem is equipment. P90X uses a larger range of weights plus pull-up bars. I know you can buy the kind that fit in doorways, but our doorways are extra tall (about 9ft), and so I would actually need a ladder to reach the bar.
If you have the time to commit to P90X, I highly recommend it. I loved it, and the workouts really get all the muscle groups, plus cardio and yoga. I really enjoy the yoga DVD, and still do it occasionally if I have the time.
You've read all the reasons why I like JMBR, but I will just add that there are several excercises she does that are also in P90X. So, I would say the routines are of similar difficulty and intensity, but Jillian takes less time to do it. She even mentions in one video that she doesn't have an hour a day to work out, so she packs it in to 30 minutes. I have not seen any of her other videos, but it seems that this workout is a little P90X inspired, unless these types of workouts are just the general trend right now.
So, both are challenging and make you work hard. If you have time to do P90X, go for it! I've known some people to lose weight and really buff up on the program. But, if you are strapped for time, yet still want a pretty intense workout, go for Jillian MIchaels. I do wish she put a challenging yoga workout in there as that always felt very beneficial in P90X, but maybe she has one on the market already. Whatever you choose, make sure it's fun for you!