Good question, and I hope I can answer it. Mind you, this is a DO talking and not a chiropracter.
First off, let me explain that I would probable fit into your "scientific chiropractor" category. Let me give you a brief history of chiropractic as compared to osteopathy. Palmer, the guy who developed chiropractic, saw Dr. Still, our founder of osteopathy, performing some of his techniques and then took what he saw and developed the first school and philosophy surrounding chiropractic medicine. It's kind of like bjj, the gracies were taught judo and then developed it into todays bjj. So when I tell people I do manipulation, they alway say "like a chiropracter?" and my answer if, no like an osteopath, chiropracters kind of stole our shtick....
Anyway, the subluxation theory of chiropractic medicine, in a nutshell, and if I am wrong, someone please correct me, but the basics are that most problems arise from a "subluxation" of a vertebrae, or a misallignment, causing dysfunction of the organ that the particular nerve inervated. Therefore, if you correct the subluxation, you allow the nerve to function fully and therefore cause resolution of the problems. Kind of like a rubber band cutting off your circulation, remove the rubber band and the blood flows.
I do not believe in this line of thinking. There is too much physiology being ignored. Lets look at coronary artery disease, all the manipulation in the world will not lower your bad cholesterol, correct high blood pressure, and reverse the damage smoking dose to the intimal layers of your coronary arteries. Type 1 diabetes is caused from the pancreas not producing insulin, manipulation is not going to change that.
Osteopathy on the other hand, believes that the musckuloskeletal portion of the body comprises over 60% of the human body, and the body has the inate ability to heal itself. And therefore, proper allignment of the musckuloskeletal system allows the body to function properly to always go to the homeostasis of health. That being said, most DOs today, don't prescribe to that line of thinking, most likely because we have been accepted as "full service" physicians that can prescribe medications, as well as do surgery. So a lot of the original osteopathic principles, althought are taught, but not necessarily followed. A lot of DO are now doing MD residencies, so the core priniciples are not emphasized.
My overall feeling are this, when all you have is a hammer, everythink looks like a nail. Chiropracters only have manipulation for treatment options, so therefore, they emphasize what they can do, for pain relief, PMS, IBS, etc. They can't prescribe medications, so a lot of chiropracters are into natural remedies and herbal treatments. But that is in the line of their teaching.
I am not anti-chiropractic, and I do feel that they provide a lot of relief, and in some cases, I do believe that manipulation can help somatic problems, PMS, IBS, fibromyalgia, etc...going back to the osteopathic prinicples, the body is going into good allignment, so health can be restored, not so much veterbrae out of whack, me fix and you better. But when it comes to infant manipulation, manipulation instead of vaccination, I am definatley opposed to that. However, I have seem some good resolution of chronic ear aches in children and gentle myofascial treatment, not the cracking, done by Dr. Viola Freeman, a DO in I believe california. Can't explain how it works, but I have seen it done. But again, some chiropracters claim treatment for ADD, and ADHD will work, and again I don't subscribe to that point of view.
Man, that is a long winded answer to your question, but I hope it helps.