In general, here clinics are private own by a doctor or group of doctors, and they treat out patients.  Some do not have much in terms of equipment, I do know a couple of them locally that do not even have an X-Ray machine, and refer you to a hospital for X-Rays, lab work, etc.  I would say doctors at clinics are mostly "generalists", or knowing a little of everything.

Hospitals are much better equiped, and have a broader range of doctors with different areas covered.  At hospitals, within the different departments, they have a staff of doctors who each is am "specialist" and concentrates only in his or her area of interest.

If you have a cold then it is OK to visit a clinic, if you have a heart attack, you will be better of in a hospital. 

It will depend mainly on what is causing you to seek medical help.

I recommend you should go to a hospital. There are numerous hospital in China. So you need to figure out what kind of specialist(dentist, psycologist,etc) you are looking for.