I would go with chiropractor every time. I had a bad back all my working life as a postman, and I have tried both. The osteopath certainly loosed me up, and straight after I felt great. However the next day I could not move.
Then I tried chiropractors, and to be honest, at first thought it was a con. People were only there a short while, forking over big money, then going. The thing is, they booked to come back.
Anyway I tried it, and before any treatment they x rayed my spine, showing it to be s shaped. Treatment only lasted a few minutes, but I did feel better. Long story short, I paid for a course of treatments, and within two months I was totally pain free and walking tall, my spine having been totally realigned.