In truth it is difficult to answer because very rarely will you find two practitioners in each of these fields who practice exactly the same way. With that said however, there are some real differences between these professions which are worth noting. They each exist for a reason because they provide a valuable service by solving different problems.
Physiotherapists tend to work with muscles and focus primarily on the region that is hurting. If you had knee pain for example they would likely massage the muscles around the knee, use technology such as ultrasound or interferential and prescribe your some home exercises to do for that joint. Physiotherapists put a big emphasis on rehabilitation of muscles. In some cases they perform spinal manipulation, which is a very different procedure to the spinal adjustments that chiropractors perform.
Osteopaths can be quite similar to chiropractors but rather than use specific ‘adjustments’ to correct spinal misalignments they tend to use long lever based ‘manipulations’ to reduce tension across joints. Osteopaths are often pain based and will generally focus their work to the area of the body that is painful.
Chiropractors are highly trained in spinal adjusting. Which rather than focussing on broad areas of the spine to reduce tension (which osteopathic and physic manipulations do), adjustments are small focussed forces designed to correct a specific misalignment of a single spinal joint. This is done with the intension of taking pressure off of a nerve. To do this correctly requires significant skill and understanding of biomechanics and neurology. This appreciation of the link between spinal alignment and the nervous system gives chiropractors a unique understanding of human health and affords a broader lens through which to assess the underlying problem(s). The pain does not necessarily give away the location of the real problem that caused it. Understanding this is where chiropractic excels.
For example, knee pain may be caused by a weakness in a thigh muscle that is further caused by pelvic and lower back misalignment which is disturbing the neurological communication between the brain and that muscle. With this muscle now weak the knee is vulnerable to injury. The real solution is therefore to correct the problem in the spine and then address the secondary issues at the knee joint. There may also be problems with this patients nutrition or exercise habits that are adding further stress in and preventing healing. The foot and ankle joints may also be a factor to be considered. This holistic understanding of health is common to practitioners of chiropractic.
Chiropractors tend to focus on overall wellness and attempt to restore as many natural conditions as possible (spinal alignment, neurology and lifestyle) to allow the body to heal. Chiropractors work from the premise that the human body is designed to be healthy and that symptoms occur because of imbalances created by an accumulation of lifestyle stresses and injuries in the body. By removing these blockages the body is then able to return to health.
Physiotherapists and Osteopaths can tend to be more medical in their approach by treating painful areas and focussing therapies directly onto them. Many chiropractors also practice with the intent to simply treat symptoms as well. There is probably a 50:50 split within the chiropractic profession between those who practice a wellness based approach and those who are symptom based. Having said that I have also met Osteopaths and Physios who are heavily wellness focussed.
To summarise there are some commonalties among the professions, they can each tend to help with the same problems, it is mostly the philosophy and mindset behind the practitioner and the types of treatments that are used which differ. Now you probably have an appreciation of the differences and why this is a challenging question to answer completely.