I haven't had sciatica but I have visited chiropractors and osteopaths with other aches and pains. In general, chirpractors concentrate on your spine; they Xray it and crunch it around to realign it (often only a millimetre or so but it can make a lot of difference). Osteopaths tend to be gentler, though they vary a lot in how they proceed. Some do a bit of crunching but they also do more massage-style work on soft tissue. Some cranial osteopaths do nothing much but hold their fingertips to your skull, which I found completely useless, but presumably other people benefit from it.
But because they vary so much it's very hard to predict how well they will treat any given problem. I've found osteopathy a grat help over the years, but some practitioners are a lot better than others.