Public vs Private Institutions
Private
When you're looking for your first teaching job in China you are likely to come across job ads from both public and private schools. There are differences between the two, and an understanding of these differences will help you make the best decision.
China's economic expansion has lead to an increase in demand for education at all levels, and the establishment of private kindergartens, schools, colleges and universities is encouraged by the government. These institutions charge relatively high fees and claim to offer better facilities and equipment, smaller classes and better teachers. One of the biggest marketing strategies for this type of school is to emphasise the size and quality of its teaching staff.
Unfortunately, these claims are not always backed up by reality. As in any sector, high demand combined with inadequate regulation causes low quality service provision. Private schools are often seen as options only for children of rich families who do not have the ability to get into the better public schools.
Teaching staff are often minimally qualified, if at all, while the modern facilities shown in glossy brochures often turn out to be 'not built yet' or rarely used. I've seen computer labs which are only unlocked when there's a photographer in the vicinity, while the pupils learn to type at their desks using cardboard mock-ups of keyboards and sports halls fall into disrepair because 'we don't have any time for sports'.
This is not to say you should avoid private institutions altogether but should be aware though that these institutions are much more driven by profit than education. This is changing, I feel, as competition for students becomes more fierce and parents become more discerning - but there's a long way to go yet . . .
The report from which the quotes above were taken is available here (PDF file)
Public
The public sector, meanwhile, is also in a state of flux. Declining government funding has led to institutions collecting fees from students, and the line between public and private is blurring somewhat. There are vast gaps in funding between remote rural areas and big cities and it would be hard to visit a rural one-teacher school and a Beijing flagship and believe that both were in the same country.
Public schools are less likely to employ foreign teachers. They place far less emphasis on English language education than private schools (though it is still a very important part of the curriculum) and are less inclined to pay the high wages foreign teachers expect. The jobs available are mainly at colleges and universities, with a few jobs at middle schools and maybe a handful at lower levels.
Students at public schools tend to be more academically successful than those at private schools - you will often meet motivated and knowledge-hungry students, although overcoming shyness and an unwillingness to contribute in class can be a problem. Facilities will vary greatly.