A chiropractor works with bone and generally entirely on the back. A physiotherapy uses machines and hands and works on the entire horse.
There are pros and cons to both. A chiropractor can provide immediate release and make your horse feel better faster but it's harder to keep and they often re-injure themselves as the adjustment isn't supported by the suddenly weak muscles. A chiropractor than knows what they're doing will always give follow up exercises. Be weary of the ones that do too many pelvic adjustments, horses can become very weary of their legs being picked up because of it. There are also a few types of chiropractor. Some believe only big movements can make a difference, some believe you only need littler and gentler adjustments.
A physio takes a bit longer to heal an injury but it tends to last. A physio will use machines such as laser, ultrasound and PEMF to do a whole range of things (which I can go into, if you'd like?). They also use massage and stretches. Some with clinics have bigger equipment such as swimming pools, treadmills etc.
If I were to pick between them, I'd go with the physiotherapist. I've nothing against a good chiropractor, it's because of one of them I'm standing upright, and I would learn it if I could.. but there's less to go wrong with a physio. However, regardless of what you choose, ALWAYS check who you are getting.
In the US, only vets can become chiropractors and physios aren't a thing so you tend to be safe enough. In the UK, your therapist should be RAMP registered, although I think AHPR is a new register that they've been building up to for a long time. However, there is still no regulation and anyone can call themselves a therapist. In Ireland, there is no register and no regulation and this is where you have to be careful. Check for qualifications, ask for references if they've been about for a while. I'm unfamiliar with other countries though.