Where to go if needed: Private hospital or State Hospital?

That is actually a hard question to answer. Both are actually really good. You will find in both excellent doctors, great assistance. The only difference will be the fee you’ll need to pay when done with each of them (High cost for private hospitals, low cost for State Hospitals). It is also worth mentioning that private hospitals usually have a special department dealing with only non-Turkish nationals, which might come handy during hard times.