I read an interesting article this morning about Clemson's Strength and Conditioning program on Shakin The Southland. The main theme of the article is comparing power lifting vs olympic lifting and which method is more effective. It's interesting how the article suggests (based on research and interviewing athletic programs around the US) olympic lifting and the benefit of using power are much greater and translate easier to athlethic performance vs how much weight can I lift.
Power Lifting uses key lifts such as bench press, squat and deadlift while Olympic lifting uses lifts such as clean, jerk and snatch. The difference is that one, the latter, not only develops strength but also fast twitch muscles which in turn help prepare for quick movements on the football field.
It's fairly technical, so you may not be interested but I do think it's a testament to Crossfit and the ideology behind it. When comparing football programs, teams using olympic lifts vs power see better results.
We can go back to the idea of what is your goal? Are you just doing strength training for aesthetic results? Or are you trying to train for a sport? Or do you just want to be healthy? If you're just doing it to have abs like Jillian, you can do either one and really need to alter your diet drastically, but for performance based results and overall functional movements, incorporating olympic lifting has been proven to yield better results.