The debate here seems to be between the benefits of pilates and full body exercises like squats deadlifts etc.
Research shows that exercises like squats and deadlifts do work your core more than pilates based exercises. However everyone is missing the point.
it is completely irrelevant which exercises work the core more, what matters is which exercises help improve running performance, and help prevent injury. So what of squats activate core more than pilates , unless it trains the core to be stronger when running then it doesnt matter. Just becasue an exercise works a muscle more doesnt mean it will help that muscle to be stronger doing something different.
The body responds to exercise based of the priciple of specific adaption to imposed demand which basically means he body gets better at ding whatever it is you do with it. So if you squat then the body will get better at squatting. If you do pilates then you get better at doing pilates.
For an exercise to benefit running it has to be similar to running - it would have to be dynamic, involve the spine moving in three different directions, light weight , high reps , similar joint ranges of movement and body position.
Unfortunately pilates and heavy squats/ deadlifts arent that similar to running so the ycarryover benefit from doing these exercises is little. ( except if you are a sprinter )
In fact studies have showed that conventional core type exercises have no measurable effect on running performance or injury prevention.
The American College of SPorts Medicine went as far as recommending that core exercises performed in a vertical position would be far more effective than ones lying down.
there is a stack of informaiton including videos of far better exercises here http://www.mile27.com.au/category/trainingthecore/
in terms of exercises like push ups, pull ups etc - in terms of running they are a waste of time ( along with crunches, sit ups, planks leg lifts etc).
however if those exercises contribute to you losing fat and decreasing overall body weight ( an upper body weight muscle increase still needs to be carried around by the legs - goof long distance runners are skiny up top for a reason) then they may be a good thing to do. Any exercise that help you lose weight will inadvertantly help make you a faster runner.
Of course if you are going to make the time to do some exercises you may as well do ones that will help your running
here are some example exercises and discussion on what is best to do for resistance training for runners
http://www.mile27.com.au/resistance-training-for-runners-part-1/
http://www.mile27.com.au/resistance-training-for-runners-part-2/
