Each of these philosophies or ideas have their own merit. To mix them is to water down each of them. Not being true to either leaves something lacking. Somethings complement each other very well, like dark chocolate and almonds go great together. Peanut butter and jelly. Hot days and the beach. Fred Astaire and Ginger Rogers. You get the idea.
Yoga and Pilates, in my opinion, are not one of these awesome relationships and should be kept separate. I'm not saying one is better than the other (oh, come on, who am I kidding--Yoga is best ;-)).
Yoga is a very complete system and has 4 to 5 thousand years behind it. Pilates has been around for the last 50 or so years, but has proven itself a very useful and beneficial system for thousands, if not millions, of people. That's impressive.
Here are some of the stats on each (based on my experience, readings, years of studying Yoga, and info from Pilates studios). Please, bare in mind, that my knowledge of Yoga is much more vast than of Pilates. I've only read a couple of books on Pilates, attending a handful of classes, and researched studio descriptions of it, but have tried my best to be fair and honest in describing each modality.
YOGA - Bhakti Yoga says that happiness comes from the Divine.
PILATES - "Physical fitness is the first requisite of happiness" - Joseph Pilates
Mind & Body
Y - In Hatha Yoga, the body is used with the breath to calm the mind and lead to meditation where the student eventually remembers his/her divine nature.
P - Physical and mental health are directly related.
Exercise only?Y - From the Yoga Sutras by Patanjali, Yoga is a lifestyle, not just an exercise.
P - Movements using machines are designed to fully engage the body and mind.
Who can do it?
Y - Can be adapted to almost anyone.
P - Can be adapted to almost anyone.
Y - Most classes focus mostly on stretching and surrender.
P - Most classes focus mostly on strength and control.
Y - Asanas (postures) are really about clearing blocks and getting the prana/energy/chi flowing.
P - There appears to be no mention of the energy system of the body.
Y - The original texts on Yoga speak a lot about life, attitude, philosophy, spirit, mind, breath, and more.
P - The Pilate texts focus mainly on the body.
Y - Yoga includes, but is not limited to the body and mind. Breath is used in pranayama to move and and direct the prana/energy inwards. Meditation and kriyas are used to affect more subtle layers (koshas) of the body, and finally the state of samadhi or nirvana is the place of complete bliss, joy, and Self-realization. (I know you just came to get rid of your back pain, but it's pretty exciting to know -- if you'd like -- you can go so much further as well!)
P - "You're only as healthy as your spine." - Joseph Pilates
Point is, just because 2 systems appear to be similar at the surface, doesn't mean rolling them into one is such a great idea. If you really have interest in both, try practicing them separately and see if you don't get more than out of one "combo" class. To cram it all into one class, just seems like too much and the real focus and benefits are lost.
One person's opinion,